It seems that AnyStr has the main advantage of ensuring that multiple arguments (or argument(s) and return values) have the same type (i.e. `str` and `bytes` are both okay but shouldn't be mixed). However it makes it significantly more difficult to cast to a single type.

With a Union, something like:

```python
def foo(a: Union[bytes, Text]) -> Text:
    if isinstance(a, bytes):
        a = a.decode()
    return "Hello, " + a
```

works fine. With AnyStr, you have to define a new intermediate variable, something like:

```python
def foo(a: AnyStr) -> str:
    if isinstance(a, bytes):
        b = a.decode()
    else:
        b = a
    return "Hello, " + b
```

If there's no advantage to using AnyStr (since there's no other AnyStr argument or return value), I think the Union would be simpler, have no significant disadvantage, and there is [precedent for similar changes](python#1054).

> It's only the case that if there's exactly one parameter of type exactly AnyStr, and no other use of AnyStr in the signature, then Union[str, bytes] should be acceptable.

-  [gvanrossum](python#439 (comment))

Discussion: 

- python#1054
- python/mypy#1141
- python#439