My neighbors' animals have fleas. That wouldn't be a problem, if we didn't share a ventilation system. Right after the temperature started to drop, and the heat kicked on, my cats ended up with fleas.

Since they're indoor cats, and I stopped taking Spot out on his leash when the dogs got fleas, the only thing I can figure is that the fleas came up through the vents.

My question is basically, how can I get rid of the fleas, if they're coming up through the vents when the heat kicks on? I can treat the cats, but that won't do any good as long as the neighbors' dogs still have fleas.

Aside from convincing them to get their pets on some type of prevention, you may have to keep yours on prevention year round.
Personally I would recommend Revolution - it seems to work excellent for cats, and if you keep up with applications, it will actually kill fleas in the environment over time. Obviously they will still get into your place but if your animals are protected they won't get too far.

I'd prefer to avoid using pesticides, if at all possible.

I don't know if there's any way to do that, but I figured it wouldn't hurt to ask.

Can you put some kind of mesh covering over the registers to allow the heat in but to trap the fleas?

I don't believe the ventilation is the reason for the continuation of the flea problem. MAYBE they came over that way, but... If this is the heating system, isn't that air coming from the furnace? Nothing there to attract fleas, and they aren't attracted to dogs or cats. They just sit and wait for dinner to be brought to them.

You most likely have been carrying fleas from the yard into your residential space on your clothes, possibly from earlier in the summer. Flea populations increase almost exponentially as time goes on, and by early Fall, they have increased to an easily 'noticed' level, inside and outside as well.

Regardless of how they got there, they are there and your thoughts should concentrate on becoming rid of them. Treating both your animals and the favorite spots they inhabit in the home are traditional approaches to this problem. You may try diatomaceous earth (food grade) on both the animals and environment. It is quite inexpensive and available at animal feed stores, or possibly the druggist (as last resort) Locally, for me, it is 50 cents a pound, and you should get away with 2 lbs worth, I'd think.

It will pour out a tube type delivery system, like a plastic bottle... not necessarily a squeeze type... that makes it more of an aerosol, and that is to be avoided. Let it be poured onto the cat's spine, from back of head to mid tail. Easily rub the fur to work it down to the skin. The top of an animal is a common place to find fleas, so eventually all the fleas will cross there and contact the DE.

Do the same with the environment the cats spend most time in. Fleas lay eggs on the animals and these fall off, hence resting (and hiding... don't forget these) areas are usually hot beds of activity. Carpets, wood floors, (even vinyl flooring), furniture (alongside the cushions). As I said, anywhere a cat goes.

The cats will act as 'magnets' for any fleas currently off the animals, so their itching will not decrease dramatically at first.

This is sort of a cursory explanation on use of DE. Check back on some older posts for similar problems with fleas for more details. Specific questions arise, feel free to ask, or IM me.