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Neon tetras are very sensitive fish, and will not do well to cycle a tank. It will take you a very long time to cycle your tank, and you will probably be doing a lot of water changes to keep your neons from getting sick. With that being said, water changes should be done according to your readings. I usually recommend that you do a water change when cycling with fish whenever the ammonia or nitrite levels gets above 1.0. However, you will probably have to do one anytime your level goes above .25 with the neons in there. They can't take less than perfect water conditions for very long. I don't usually recommend this to newbies because cycling a tank is the most important lesson you will learn in the hobby, but since you already have fish in the tank, and sensitive fish at that, look around locally for bio spira at a reputable fish store. Bio spira contains the bacteria needed to have a cycled tank. If you can find some, and are willing to pay the high price for it, get some, and make sure the store is reputable, or you might end up with an expensive bottle of dead bacteria. You will also have to decide what other fish you will have in your tank, buy them, and add them to the tank also. Bio spira works best when added along with a full bio load of fish. If you have any ammonia or nitrite levels in your tank before adding the bio spira, you will probably have to do a large water change before adding the bio spira and the fish.
Let us know what you are gonna do so we can help you along with this. Please post what other fish you plan to put in your tank with the neons.