Like most departments, they were part of the mutual aid system for NY State, where neighboring departments assist each other during major alarms, be it at the scene or standing by at the requesting station in case of a second unrelated alarm. The slang term for a really big alarm was Southern Mutual Aid (Y'all come).
Alas, Katerina adds new to meaning to this. As reported by the Wall Street Journal's Evelina Shmukler and Peter Sanders reporting from Mississippi's Gulf Coast:
It's easy to get a little lost in Mississippi these days. The influx of rescue, law enforcement, utility and other support crews from all over the country can mean some surreal moments. On Interstate 10, a Miami police cruiser flies by, lights flashing. A New York Police Department vehicle drives down the beachfront road in Gulfport, as does a search and rescue crew from Salt Lake City. The North Charleston Police Department is directing traffic in North Biloxi. A Georgia Bureau of Investigation officer sits across from the Harrison County emergency operations center.