Fuel Pump

You'd need to check fuel pressure. You need to be sure of spark too. If the car starts, but then quits repeatedly, than it would seem the fuel pump and fuel pump relay are working but only during startup or pressurization before startup and not working running. I think you need to tow the car to a Mazda specialist. Also, when you call someone or write in, please tell which engine you have, they are quite different. Here's a directory link for you: https://repairpal.com/mazda-repair-in-greenbelt-maryland