REGA 3- Sounds better with dust cover ON of OFF ?

Don't know specifically about the Rega, but the general rule is -- dustcover off. Best answer -- listen for yourself and decide.
--Neil

Rega says it's best with it on. My experience is totally contrary. Their alignment protractor puts the cartridge in the wrong place as well. What do you want from a company that says it is unnecessary to clean your records? I have owned a Planar 3 for many years and currently own a P3 and have experimented with both.

I expierimented with having the cover on and off on my Rega P25 and liked the results better with my cover off. It seemed to "open" things up. Probably all in my head...but try it...it is a cheap mod.

If you leave it just open it wouldn't do any trick compared to the closed one. For the audiable difference remove it with hinges together(I know it's pain to place it back when you need to keep it closed other times).