The private maker of an anti-choking device and a Long Island-based nonprofit communicated closely with a city council member’s office last year as that lawmaker pushed to require anti-choking devices in all city schools despite recent warnings from leading medical authorities. Anti-choking or airway clearance devices have grown in popularity in recent years, with success stories gaining traction on social media. The devices are placed over a choking victim’s nose and mouth to create suction.