How can I transport Mac Pro 2013?

Apple had enough confidence in its ability to operate and cool itself (a bit differently than normal, perhaps) in a Horizontal position, that they allow you to run it that way. There are aftermarket rack mount setups that place the unit horizontally on a rack-mount "drawer".

For transport, It does not need to be kept vertical, or even right-side-up.

Horizontal should work... are expecting exceptionally bumpy ride?

Good luck my friend. :)