diff --git a/akernel/akernel.py b/akernel/akernel.py
index 8313fbc..9df1a17 100644
--- a/akernel/akernel.py
+++ b/akernel/akernel.py
@@ -16,14 +16,14 @@ def install(
         None, "-c", help="Path to the cache directory, if mode is 'cache'."
     ),
 ):
-    name = "akernel"
+    kernel_name = "akernel"
     if mode:
         modes = mode.split("-")
         modes.sort()
         mode = "-".join(modes)
-        name += f"-{mode}"
-    display_name = f"Python 3 ({name})"
-    write_kernelspec(name, mode, display_name, cache_dir)
+        kernel_name += f"-{mode}"
+    display_name = f"Python 3 ({kernel_name})"
+    write_kernelspec(kernel_name, mode, display_name, cache_dir)
 
 
 @cli.command()
diff --git a/akernel/cache.py b/akernel/cache.py
index 6be5ee2..3d5361b 100644
--- a/akernel/cache.py
+++ b/akernel/cache.py
@@ -1,13 +1,14 @@
+from __future__ import annotations
+
 import os
 import pickle
 import sys
 import zlib
-from typing import Optional
 
 from zict import File, Func, LRU  # type: ignore
 
 
-def cache(cache_dir: Optional[str]):
+def cache(cache_dir: str | None):
     if not cache_dir:
         cache_dir = os.path.join(
             sys.prefix, "share", "jupyter", "kernels", "akernel", "cache"
diff --git a/akernel/code.py b/akernel/code.py
index 80dec3c..43b11fd 100644
--- a/akernel/code.py
+++ b/akernel/code.py
@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 import copy
 
 import gast  # type: ignore
@@ -90,8 +92,9 @@ def get_return_body(val):
 
 
 class Transform:
-    def __init__(self, code: str, react: bool = False) -> None:
+    def __init__(self, code: str, task_i: int | None = None, react: bool = False) -> None:
         self.gtree = gast.parse(code)
+        self.task_i = task_i
         self.react = react
         c = GlobalUseCollector()
         c.visit(self.gtree)
@@ -115,9 +118,10 @@ def get_async_ast(self) -> gast.Module:
             new_body += self.gtree.body + body_globals_update_locals + last_statement
         else:
             new_body += self.gtree.body + body_globals_update_locals
+        name = "__async_cell__" if self.task_i is None else f"__async_cell{self.task_i}__"
         body = [
             gast.AsyncFunctionDef(
-                name="__async_cell__",
+                name=name,
                 args=gast.arguments(
                     args=[],
                     posonlyargs=[],
diff --git a/akernel/execution.py b/akernel/execution.py
index bb01090..bea45eb 100644
--- a/akernel/execution.py
+++ b/akernel/execution.py
@@ -1,6 +1,8 @@
+from __future__ import annotations
+
 import hashlib
 import pickle
-from typing import List, Dict, Tuple, Any, Optional
+from typing import List, Dict, Tuple, Any
 
 from colorama import Fore, Style  # type: ignore
 
@@ -12,16 +14,17 @@ def pre_execute(
     code: str,
     globals_: Dict[str, Any],
     locals_: Dict[str, Any],
+    task_i: int | None = None,
     execution_count: int = 0,
     react: bool = False,
-    cache: Optional[Dict[str, Any]] = None,
-) -> Tuple[List[str], Optional[SyntaxError], Dict[str, Any]]:
+    cache: Dict[str, Any] | None = None,
+) -> Tuple[List[str], SyntaxError | None, Dict[str, Any]]:
     traceback = []
     exception = None
     cache_info: Dict[str, Any] = {"cached": False}
 
     try:
-        transform = Transform(code, react)
+        transform = Transform(code, task_i, react)
         async_bytecode = transform.get_async_bytecode()
         exec(async_bytecode, globals_, locals_)
     except SyntaxError as e:
@@ -100,7 +103,7 @@ def pre_execute(
 
 
 def cache_execution(
-    cache: Optional[Dict[str, Any]],
+    cache: Dict[str, Any] | None,
     cache_info: Dict[str, Any],
     globals_: Dict[str, Any],
     result: Any,
@@ -132,9 +135,8 @@ async def execute(
     code: str,
     globals_: Dict[str, Any],
     locals_: Dict[str, Any],
-    chain: bool = False,
     react: bool = False,
-    cache: Optional[Dict[str, Any]] = None,
+    cache: Dict[str, Any] | None = None,
 ) -> Tuple[Any, List[str], bool]:
     result = None
     interrupted = False
@@ -147,8 +149,6 @@ async def execute(
     if cache_info["cached"]:
         result = cache_info["result"]
     else:
-        if chain:
-            await locals_["__task__"]()
         try:
             result = await locals_["__async_cell__"]()
         except KeyboardInterrupt:
diff --git a/akernel/kernel.py b/akernel/kernel.py
index ee24b03..e6db2cf 100644
--- a/akernel/kernel.py
+++ b/akernel/kernel.py
@@ -4,7 +4,7 @@
 import json
 from io import StringIO
 from contextvars import ContextVar
-from typing import Dict, Any, List, Optional, Union, Awaitable, cast
+from typing import Dict, Any, List, Union, Awaitable, cast
 
 from zmq.asyncio import Socket
 import comm  # type: ignore
@@ -41,22 +41,23 @@ class Kernel:
     key: str
     comm_manager: CommManager
     kernel_mode: str
+    cell_done: Dict[int, asyncio.Event]
     running_cells: Dict[int, asyncio.Task]
     task_i: int
     execution_count: int
     execution_state: str
     globals: Dict[str, Dict[str, Any]]
     locals: Dict[str, Dict[str, Any]]
-    _multi_kernel: Optional[bool]
-    _cache_kernel: Optional[bool]
-    _react_kernel: Optional[bool]
+    _multi_kernel: bool | None
+    _cache_kernel: bool | None
+    _react_kernel: bool | None
     kernel_initialized: List[str]
-    cache: Optional[Dict[str, Any]]
+    cache: Dict[str, Any] | None
 
     def __init__(
         self,
         kernel_mode: str,
-        cache_dir: Optional[str],
+        cache_dir: str | None,
         connection_file: str,
     ):
         global KERNEL
@@ -78,6 +79,7 @@ def get_comm_manager():
         self.globals = {}
         self.locals = {}
         self._chain_execution = not self.concurrent_kernel
+        self.cell_done = {}
         self.running_cells = {}
         self.task_i = 0
         self.execution_count = 1
@@ -258,6 +260,7 @@ async def listen_shell(self) -> None:
                     code,
                     self.globals[namespace],
                     self.locals[namespace],
+                    self.task_i,
                     self.execution_count,
                     react=self.react_kernel,
                     cache=self.cache,
@@ -289,6 +292,7 @@ async def listen_shell(self) -> None:
                             cache_info,
                         )
                     )
+                    self.cell_done[self.task_i] = asyncio.Event()
                     self.running_cells[self.task_i] = task
                     self.task_i += 1
                     self.execution_count += 1
@@ -353,15 +357,17 @@ async def execute_and_finish(
         code: str,
         cache_info: Dict[str, Any],
     ) -> None:
-        if self._chain_execution:
-            await self.task()
+        prev_task_i = task_i - 1
+        if self._chain_execution and prev_task_i in self.cell_done:
+            await self.cell_done[prev_task_i].wait()
+            del self.cell_done[prev_task_i]
         PARENT_VAR.set(parent)
         IDENTS_VAR.set(idents)
         parent_header = parent["header"]
         traceback, exception = [], None
         namespace = self.get_namespace(parent_header)
         try:
-            result = await self.locals[namespace]["__async_cell__"]()
+            result = await self.locals[namespace][f"__async_cell{task_i}__"]()
         except KeyboardInterrupt:
             self.interrupt()
         except Exception as e:
@@ -371,6 +377,8 @@ async def execute_and_finish(
             self.show_result(result, self.globals[namespace], parent_header)
             cache_execution(self.cache, cache_info, self.globals[namespace], result)
         finally:
+            self.cell_done[task_i].set()
+            del self.locals[namespace][f"__async_cell{task_i}__"]
             self.finish_execution(
                 idents,
                 parent_header,
@@ -385,8 +393,8 @@ def finish_execution(
         self,
         idents: List[bytes],
         parent_header: Dict[str, Any],
-        execution_count: Optional[int],
-        exception: Optional[Exception] = None,
+        execution_count: int | None,
+        exception: Exception | None = None,
         no_exec: bool = False,
         traceback: List[str] = [],
         result=None,
diff --git a/akernel/kernelspec.py b/akernel/kernelspec.py
index b245a45..c0a8644 100644
--- a/akernel/kernelspec.py
+++ b/akernel/kernelspec.py
@@ -1,11 +1,12 @@
+from __future__ import annotations
+
 import os
 import sys
 import json
-from typing import Optional
 
 
 def write_kernelspec(
-    dir_name: str, mode: str, display_name: str, cache_dir: Optional[str]
+    dir_name: str, mode: str, display_name: str, cache_dir: str | None
 ) -> None:
     argv = ["akernel", "launch"]
     if mode:
diff --git a/akernel/message.py b/akernel/message.py
index d9d313e..730103a 100644
--- a/akernel/message.py
+++ b/akernel/message.py
@@ -2,7 +2,7 @@
 import hmac
 import hashlib
 from datetime import datetime, timezone
-from typing import List, Dict, Tuple, Any, Optional, cast
+from typing import List, Dict, Tuple, Any, cast
 
 from zmq.utils import jsonapi
 from zmq.asyncio import Socket
@@ -86,7 +86,7 @@ def serialize(msg: Dict[str, Any], key: str, address: bytes = b"") -> List[bytes
 
 async def receive_message(
     sock: Socket, timeout: float = float("inf")
-) -> Optional[Tuple[List[bytes], Dict[str, Any]]]:
+) -> Tuple[List[bytes], Dict[str, Any]] | None:
     timeout *= 1000  # in ms
     ready = await sock.poll(timeout)
     if ready:
@@ -101,7 +101,7 @@ def send_message(
     sock: Socket,
     key: str,
     address: bytes = b"",
-    buffers: Optional[List] = None,
+    buffers: List | None = None,
 ) -> None:
     to_send = serialize(msg, key, address)
     buffers = buffers or []
diff --git a/akernel/tests/conftest.py b/akernel/tests/conftest.py
index fc53e83..cc0447b 100644
--- a/akernel/tests/conftest.py
+++ b/akernel/tests/conftest.py
@@ -12,6 +12,9 @@ def all_modes(request):
     mode = request.param
     kernel_name = "akernel"
     if mode:
+        modes = mode.split("-")
+        modes.sort()
+        mode = "-".join(modes)
         kernel_name += f"-{mode}"
     if mode == "cache":
         cache_dir = os.path.join(
@@ -19,4 +22,4 @@ def all_modes(request):
         )
         shutil.rmtree(cache_dir, ignore_errors=True)
     display_name = f"Python 3 ({kernel_name})"
-    write_kernelspec("akernel", mode, display_name, None)
+    write_kernelspec(kernel_name, mode, display_name, None)
diff --git a/akernel/tests/test_execution.py b/akernel/tests/test_execution.py
index b0e4a5a..9bd81c4 100644
--- a/akernel/tests/test_execution.py
+++ b/akernel/tests/test_execution.py
@@ -1,9 +1,11 @@
+from __future__ import annotations
+
 import sys
 import time
 from textwrap import dedent
 import re
 from math import sin
-from typing import List, Dict, Tuple, Any, Optional
+from typing import List, Dict, Tuple, Any
 
 import pytest
 
@@ -12,16 +14,15 @@
 
 async def run(
     code: str,
-    globals_: Optional[Dict[str, Any]] = None,
-    chain: bool = False,
+    globals_: Dict[str, Any] | None = None,
     react: bool = False,
-    cache: Optional[Dict[str, Any]] = None,
+    cache: Dict[str, Any] | None = None,
 ) -> Tuple[Any, List[str], bool, Dict[str, Any], Dict[str, Any]]:
     if globals_ is None:
         globals_ = {}
     locals_: Dict[str, Any] = {}
     result, traceback, interrupted = await execute(
-        code, globals_, locals_, chain=chain, react=react, cache=cache
+        code, globals_, locals_, react=react, cache=cache
     )
     if "__builtins__" in globals_:
         del globals_["__builtins__"]
diff --git a/akernel/traceback.py b/akernel/traceback.py
index e4e6791..baa1b89 100644
--- a/akernel/traceback.py
+++ b/akernel/traceback.py
@@ -1,6 +1,8 @@
+from __future__ import annotations
+
 import sys
 import types
-from typing import Optional, cast
+from typing import cast
 
 from colorama import Fore, Style  # type: ignore
 
@@ -13,7 +15,7 @@ def get_traceback(code: str, exception, execution_count: int = 0):
             break
         tb = tb.tb_next
     stack = []
-    frame: Optional[types.FrameType] = tb.tb_frame
+    frame: types.FrameType | None = tb.tb_frame
     while True:
         assert frame is not None
         stack.append(frame)
@@ -31,7 +33,7 @@ def get_traceback(code: str, exception, execution_count: int = 0):
             with open(filename) as f:
                 code = f.read()
             filename = f"{Fore.CYAN}File{Style.RESET_ALL} {Fore.GREEN}{filename}{Style.RESET_ALL}"
-        if frame.f_code.co_name == "__async_cell__":
+        if frame.f_code.co_name.startswith("__async_cell"):
             name = "<module>"
         else:
             name = frame.f_code.co_name