history of effects

No, not at all. For a start, Audition doesn't open MP3 files as such, it decodes them to wav files. What you do to them then is only stored as a sequence of temporary Audition files that you can step back though, and the moment you save the file, that information is deleted - otherwise you'd end up with a drive entirely full of useless temp files in no time.

And then, after you've done whatever you are going to, you're going to save it as an MP3 again, so it's going to get re-encoded. No information transfers with that either, as there's no provision within the metadata to store anything like that at all. And there's a reason for that...

And that is because MP3 files are distribution files intended for finished work only - not production purposes. Any processing that's happened to it is essentially irrelevant.

Also you should note that every time you open, alter and resave an MP3 file in Audition, it loses quality because of the decode-re-encode process - often quite noticeably if it started out as 128k. It's fine to open one and play it, and then close it again without altering it, but that's all.