Looking on the internet deeply has found these results:

by air is the most popular phrase on the web.

By thin air 120,400 results on the web	by air 135,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	One controversy centred on the policy of not dropping supplies by air. Fresh fishery products and consignments arriving by air, road or rail require a shorter period than three working days. The only entrance and exit Juneau is by air or sea. Simplified procedures for transport by air . Bombs were hidden inside live dogs that were to be sent by air to the US. Smallpox can be transmitted by air. You travelled to Belfast, by air, on August the 2nd. They traveled 60 minutes by air.

By thin air

120,400 results on the web

by air

135,000,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

One controversy centred on the policy of not dropping supplies by air.
Fresh fishery products and consignments arriving by air, road or rail require a shorter period than three working days.
The only entrance and exit Juneau is by air or sea.
Simplified procedures for transport by air .
Bombs were hidden inside live dogs that were to be sent by air to the US.
Smallpox can be transmitted by air.
You travelled to Belfast, by air, on August the 2nd.
They traveled 60 minutes by air.