Equalizer in a Hi Fi system

A question as it pertains to analog EQ like Loki(s).  Is any (if any) phase shifting at the band used an on/off effect with a setting other than zero, or is phase change relative to the level used?  Also, if EQ is operating on the whole input (not left/right) would you hear any possible phase shift that degrades imaging? L/R channel phase changes seem obviously an issue.

To blanket say that digital EQ doesn't affect phase or have "any artifacts" seems a stretch.  I suppose it's possible if the design of hardware and any algorithms account for it with the highest level of effort.  In my previous life, with algorithms that work as DSP, and not even in real time, but as a computer run in background (all the time needed), any spectral processing still had a phase change. 

Wouldn't this assumption be on par with "ones and zeros are ones and zeros"?

I use 2 lokius, one each channel for asymmetrical needs.  They have full bypass switch.  Even engaged I cannot "hear" them.  One poster here recently chose Lokius over Loki max based on what he heard.  YMMV.  Having independent L/R is really nice IMHO (listen up Schiit).