To further beat a long dead horse:
Actually the laser we used was a battery powered 10 amp gyro stabilized to vertical unit on a tripod so straight up was straight up. It was best to check with a small level on the lens on a cold day as it sometimes froze off level and straight up wasn't - the surveyor would sometimes do his thing and then ask you to climb or descend on the beam to confirm that you were indeed going straight up or down.
If you set up in a swamp and someone walked near the laser you would actualy see the beam start to jiggle and a quick call on the radio to have the person stop moving around was needed.
When the surveyor ( located miles away saw us appear over the hill he would tell us to stop climbing and we would hold postion on the laser Dot in the TV screen and altitute with the altimeter.) Holding altitude once hover was achieved was not a problem - at least the surveyors never complained.
Once the shot was done we would descend - not looking down at the laser of course and pick it all up then move to the next turning point and do it all over again.
Anyhoo - all done a long time ago in a Power project far far away.