zz, ‘change of property’
This is normally associated with money and lawyers.
A Euro built (not Airbus) aircraft, US owned, could be delivered with a mixed crew - operators and manufacturer under part 91. A particularly useful option with a multiple stop delivery route so to keep the aircraft moving.
Alternatively a Euro built, owned, and crewed aircraft could be delivered to a suitable location for import but not necessarily change of ownership. For GA aircraft this often involved obscure airports / states to gain the relevant tax advantage - 100lbs of fuel please to prove that we were here. After ‘import’ the same crew delivered the aircraft to destination / completion centre.
AFAIK change of ownership mid air would be illegal because all aircraft carry a unique fireproof plate indicating a specific ownership (accident scenario).
For an en route change of ownership, once the money is in place then a plate change is done during a tech stop, and the aircraft continues to destination. The above legality implies that the alternative plate of ownership is not on the aircraft during transit, but then who knows ....
Re ‘unionised’ pilots; from distant memories, Airbus pilots were all but independent company employees, I don’t recall any ideas of unions - they get in the way of doing the job.
Some company pilots, e.g. training Capts (Airbus not known) may have belonged to a generic union, but AFAIR this never became involved with the manufacturer.