I believe it is the Nitrogen cycle although all of the cycles use bacteria. Only nitrogen requires nitrogen fixing bacteria to keep the cycle going.
A filter is a device that can reduce particulate in gaseous emissions from mobile exhausts. Specifically known as diesel particulate filter (DPF) removes soot from gasses of the diesel engine through the exhaust. It significantly reduces the amount of pollutants present in the air.
What the other three events before were so you can check yourself with the photo
