Lately a few musician friends discussed transposition in relation to perfect pitch (absolute pitch) and relative pitch. Some say musicians with perfect pitch have more trouble transposing than those with only relative pitch.
Here I share some of my takes, particular on some of common myths. Here's my disclaimer though: my empirical experiences may or may not match with some cognitive models, let alone what's really going on in the brains. However, I am confident enough to say, what I summarize here has been proved practical by myself and many of my fellow musicians.
I recommend reading Wikipedia on the pitch topic for better understanding of the topic and the its various issues. Here I merely provide some of my personal experiences.