The following chords correspond to both A# and Bb. Even though it says A#7, it's the same as Bb7.A#m is the same as Bbm, and so on.
You should be aware of that if you are reading a chordbook written by non-English/American authors (ie authors using H instead of B) a B is in fact A#/Bb. I know it is a bit messy, therefore it's easier to use B instead of H
As you may or may not know the H is derived from nothing but a misreading mistake by a monk in the 16th century (that's why it's not logical).
Keep in mind that there is no such thing as "H flat" - this would simply be a B in the old school notation.