Breaking the aircraft down
Immersive Aircraft vehicles are assembled from parts, so the cleanest way to move one is to disassemble it. Dismount first, then break the aircraft block or the individual components (
engine, 
propeller, 
hull, and so on) with the correct tool. Each part drops as an item you can pick up and carry in your inventory. If you break the main aircraft block, the whole thing usually collapses back into its component items, which is the fastest way to relocate a large build.
Reassembling elsewhere
Carry the parts to your new location and place them back in the same arrangement — hull first, then engine, propeller, and any extras like gyroscopes or weapons. Gyroscopes matter here: an aircraft without a working 
gyroscope will be unstable or refuse to fly properly, so do not forget to reattach it. If you only need to nudge a plane a short distance, you can often push or tow it while it is parked, but for anything longer than a few blocks, disassembly is safer than dragging a fragile frame across terrain.