Never mind, just translate for us. please.
Everybody does things a little differently, but...
I’m guessing “bearcat” is an armored vehicle. LAPD used to have one they could mount a battering ram on. Shortly after it arrived, they started their operation, which probably consists of clearing buildings one at a time unless they’ve pinned the guy’s location. If they’ve located him, they’ll PA him to come out, then go for the gas.
That ‘hold the air’ involves an emergent incident, probably somewhere else. They’ll keep the frequency clear until it’s resolved.