Denoting bijection (conjugation) in a commutative diagram

Question

I have a simple notation question: I there a standard way how to denote in a commutative diagram that a map is a conjugation? I thought of the following three, but:

1. The left one (simple arrow) doesn't show that $\psi$ is invertible
2. The middle one (double-ended arrow) doesn't make it clear that $\psi\colon X_{\sf S}\to X_{\sf B}$ and not the other way around
3. I didn't find any reference that the right one (two harpoons) would be actually used.

Note that I'm not doing category theory, this is in symbolic dynamics. So, is there any standard way how to denote this? Even if the right one were non-standard, is there a reason why not to use it?