So, let's say that one of your filter sponges is ruined. You need to replace it but it will cause a mini or full cycle. Here's how you can:
Get a bucket or container big enough to hold your new & old media, as well as at least a gallon of water. Next put your water, old & new media in there and an air pump. Switch the pump on to get some circulation going. Then squeeze out the old media. Leave this bucket sitting for at least a week. To speed the process up, dip the new media in 1ppm ammonia.
When the process is finished, quickly add the new media.
Here's what's going on.
The sponge is a megacity of bacteria that eat harmful particles such as ammonia or nitrite. If you replace the sponge, all the bacteria is lost and there is nothing to eat the harmful particles which could kill your animals. By doing this method, you are giving the bacteria time to flock over to the new sponge.
It would be best to have two filters in this scenario so that there is still something cleaning the tank.