Lets take this back just a step - to the basics and see if I can make it a bit clearer.
When we refer to a tank's "cycle" we are refering to the process that takes the fish's waste and turns it into a less toxic substance that you can then remove from your tank's water by regular water changes to dilute the substance down.
A fish makes ammonia. That is its waste. Ammonia in the tank's water is toxic to the fish. The ammonia is processed into nitrIte, a toxic substance, too. The nitrIte is then processed into nitrAte - a substance that is not as toxic. Since the nitrate cannot be processed and does not go anywhere, as more and more ammonia is made into nitrIte and then into nitrAte, the nitrAte concentrations in the water will build and build, until there is too much nitrAte in the water for the fish to be healthy. To reduce the amount of nitrAte in your water, you remove it by removing a portion of your water and replacing it with water that has no nitrAte in it.
It is this process that is called the "nitrogen cycle" or the changing of the fish's waste into a less toxic substance. A tank that is "cycled" means it is set so that it can process all the waste that the fish in the tank produce. A tank that is "cycling" means that it is not yet capable of processing all the waste from the resident fish.
The way the cycle works is through the use of bacteria - good bacteria that reside in your filter. There are two types of bacteria. One type processes all the ammonia into nitrIte. It uses oxygen and ammonia to make nitrIte.
The second type of bacteria will process the nitrIte into nitrAte, also using oxygen.
You then will change out some water to lower the amount of nitrAte in your tank.
When you are doing a fishless cycle - or building the colonies of beneficial bacteria to process the ammonia and consequently, nitrIte, you do not have to worry about the toxic amounts of ammonia or nitrIte or even the amounts of nitrAte that are in the water during the time it takes for the bacteria to grow and work. There are no fish to harm. So you just let it go.
First the type of bacteria that processes the ammonia to nitrite will grow. They will make loads of nitrite in the tank. The presence of this nitrite will encourage the second type of bacteria to grow - the type that will change the nitrIte into nitrate.
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When you have a cycled tank - a tank that is processing all your fish's waste - you will need to do water changes approximately once a week to reduce the concentrations of nitrAte - the final nitrogen stage of the waste. NitrAte values of over 40ppm or so can bother fish - some fish more than others. High nitrAtes can lead to lower immunities, poor breeding, SBD and a few other problems. To remove the nitrAte, you will remove a portion of the tank's water and replace it with nitrAte free water.
The beneficial bacteria that make up your cycle are not in your water - they reside on the bio media you have placed in your filter - the sponge or ceramic cylindars or sintered glass or bioballs or whatever. When you do a water change, do not be afraid to change out whatever volume of water you need to to reduce the nitrAtes to where you want them. I rarely do a water change of less than 50% - most are 50%. I like big water changes. They work for me and my tanks. This changing will not harm, change or stunt your cycle..... the bacteria are not harmed in any way.
For example, if a tank of mine reads 40ppm nitrates, and I change 50% of the water, I will only have reduced the nitrates to 20ppm. I, personally, like it to be at about 5ppm or so, so I would change out about 75% of the water, or I would change the water more often than once a week to keep the nitrates lower.
I do NOT change the filter media. I rinse the media out in used fish water to remove the waste, but the beneficial bacteria will remain if you do not use any water that is different pH, or contains chlorine or whatever from your tap. The filter is where the cycle resides and it stays just fine.
Even though I do large water changes, I never do a 100% water change. This is not necessary. Of course - there are times when a tank is moved or something is being changed in my system that I change out 100% - but that is not the norm. There is no need to regularly change out 100% of your water - the tank will be just fine - in fact will be better for it - if you simply change the amount that you need to, to keep the nitrAte values where you wish them to be.