My mistake about CUZ, I meant it receives flights from Bolivia.

There were few international airports 20 years ago, including Iquitos. Not sure why they closed the international connections then.

Yes doing a deeper research I find Arequipa has Sky Airline and other small airlines flights to Chile. And it's an "Aeropuerto International". However I don't know why is not so promoted and there are no LAN, Copa, or Taca flights (or US airlines).

Piura does not show the "Aeropuerto International" title in the Corpac website, though I see there were some TAME flights to Ecuador. But Aeropuertos del Peru website includes only LAN, Peruvian and TACA as regular airlines (and I think those are domestics) for the Piura airport.

In general there are no main connections to other Peru airports, from international large airlines. Due to weather conditions, some international airlines land in Pisco or Chiclayo instead of Lima but those are exceptional landings. But thinking in regular flights, there is no advertisement of direct flights to other peruvian destinies. The Copa to Iquitos is the first one I read in a long time.