An Airnode is owned and operated by an API provider. Every Airnode has a unique on-chain airnodeAddress created and known by its API provider. API providers normally announce their Airnode addresses in the form of a DNS TXT record within their DNS registration, which also serves to prove ownership. An API provider's Airnode address is the same for all chains.
The key for the TXT record is chainapi-verification-keys and is an array of Airnode addresses owned by the API provider. Below is an example of the Airnode for dxFeed.