Why does Anthrax use e flat tuning live when the albums are in standard tuning?

#1
The question speaks for itself. I know that on fist full of metal all the way up to persistence of time (not sure about the other albums) the guitars/bass are in standard e tuning but when Anthrax plays live they tune a half step flat. What is the point of doing this and why do it?
#2
Slayer has done this and quite a few other bands have as well, as far as I know. 

I assume it has to do with convenience. Just play in one tuning for a few of the same songs and you don't have to keep swapping guitars/tunings back and forth every song.