Cycles; not cycle.
First, ammonia oxidation and nitrate oxidation to nitrate, this is the nitrification cycle. This is the most critcial as ammonia is toxic to fish and other organisms.Tpically a tank is safe for marine animals when ammonia is zero.
Then the denitrification ,ie, nitrate(NO3) is reduced to N as bacteria engaged in anerobic activity take the O in areas where free O is unavailable. The N then combines with N to form N2 nitrogen gas which bubbles out . This can take months to become fully established. Some tanks may never have enough anaerobic nitrogen reduction to keep up with nitrogen inputs from food, etc. Some, boost heterotrophic bacteria via organic carbon dosing to match high N inputs;some use macro algae ;some deep sand beds or extra live rock to provide more hypoxic (low oxygen ) areas.