I've moved mine twice. I did it once standing up and once laying down. No problems either way. When it was stood up, I had other stuff packed around it, and I strapped it down.
I once knocked the whole saw over, hard, while cutting up an osage log. Knocked it all out of kilter, but didn't break anything. I just loosened the bolts that hold the top and bottom frame halves together, and moved it back towards where it was until the blade tracked good again.