'keep up appearances'
'hold onto their self-respect'
'cover their asses'

Seems to me that these are by no means synonyms or poecilonyms for one another.

"Keeping up appearances" implies a certain dishonesty, that things are not as they appear. Usually applied to people who are trying (with limited success) to "keep up with the Joneses".

"Holding on to self-respect" implies struggling rather nobly in the face of adversity. Wearing rags, but clean rags.

"Covering your arse" is quite similar to covering your tracks, leaving nothing to connect you with what some may see as dodgy dealings. It's usually sensible, but isn't generally something of which people are openly proud.