Exhale

Out with the bad air.

There's nothing like a blast of vacuum to clean out those air cores. Don't forget to switch on the secondary life-support system.

You need to lock down the flow-gates to living area's (which is any place that's not an air core really) and flush the cores with cleanser (a nice toxic and corrosive gas with a short half-life), then shoot all the loose trash into space.

In with the good air.

There'll be more bugs and rats in a bit, and you'll need to feed more cats for a while. Log it and move on to the next core.