Only Gram-Positive bacilli bacteria are able to form spores (what I assume you mean by cysts), and those bacteria only form spores when they run out of nutrients. They won't form spores if the temperature changes to a lethal level, or if they dry out, unless they run out of nutrients at the same time.
The nitrogen oxidizing bacteria that are used to for your biological filter are Gram-negative and bacillus I think. I know for sure that they are Gram-negative, I just can't find their exact shape.
Anyways, they won't form spores
When the bacteria dries out, it is dead.
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