Since AS markers can only appear during the combat phase (as a result of barrage) the only movement, per se, is retreat due to barrage or GA. In the first case, AS markers stay with units as they retreat (and retreating from barrage requires the placement of an additional AS marker -up to two per stack. After each GA, you can remove the AS markers from units that participated in that GA (attacking and defending) as they will no longer have any effect and are removed at the end of that Combat Phase anyway.
Just to clarify, Joe.
Rule 11.7.2 Numerical Hits Note 3. If does not already have an AS marker, it will gain one when it retreats.
Which of these is true?
a) A unit that retreats as a result of bombardment gains an AS counter
b) A unit that retreats as a result of bombardment gains an AS counter if it does not already have an AS counter.