Carrier heater blower fan keeps running after the gas turns off.

The fan should run for a period of tome after the thermostat has been satisfied, usually around 90 seconds which feels like hours. If the fan still stays on, check your thermostat... is it in the ON position? Also, after that... you should look toward the furnace control board or the fan relay. If it's somewhat newer furnace it probably has a circuit board that turns the fan on and off... if it's a real old one, you might have an actual fan relay control of limit switch .