The right cleaning tool can make the difference between a cumbersome chore and a smooth one.We’ve put dozens of vacuums, mops, and carpet washers through heavy-duty cleaning tests, with bags full of pet hair, jars of peanut butter and Nutella, and the most pernicious mess of all, packets of glitter.But even when we find a price cut on a cleaner that aced our rigorous tests, it still might not be a worthwhile discount. And most so-called “deals” you’ll come across this week are for products that aren’t that great to begin with. Our full-time deal hunters know when you’re better off holding out for a lower price, especially with Black Friday on the horizon.Here, we’ve rounded up all of the best Prime Big Deal Days discounts on cleaning workhorses from vacuums to air purifiers. You can trust that everything on this page has been independently tested and vetted — and is actually worth it.