Sorry to jump in - I think Crab's saying that any change in collective pitch applies immediately and equally to all blades in terms of pitch angle.
Coefficient of lift is basically directly proportional to angle of attack anywhere below the onset of the stall, so with all other things being equal except speed (the advancing blade being quicker than the retreating one in forward flight of course), a given pitch angle increase will give you more of a lift increase on the advancing side than on the retreating side. Due to phase lag that will manifest itself as a pitch up (or conversely a pitch down if you're dumping the collective).
Once the rate of climb or descent builds up, then the effect of aerodynamic surfaces behind the center of gravity (e.g. stab / elevator, and tail boom itself) will act in the same way - pitch down for a descent, pitch up for a climb.