Lin explained it pretty well.
im only going to add, to search for progressed moon transiting 4th house cusp, i've seen it countless times.
Moon (the progressed) is the one i search for this type of things, because it literally means change.
Definitely agree with prog moon transiting 4th. Also transit jupiter transiting natal 4th for moving far, or moving to larger home. Possibly uranus entering 9th house for long distance moves.