Our experience proves that ozone treatment and biological filtration support each other very much. Huckstedt already wrote about this in 1960:
It should be discussed whether ozone treatment and biological activity of bacteria cooperate. The suspicion that by ozone treatment not only the harmful but also the useful bacteria (nitrification bacteria for instance) could be killed is quite obvious. But strange enough this is unfounded. Either these bacteria are not in the free water but mostly at the bottom of the aquarium or on the algae or they grow faster than they die. Probably both versions are correct. It can definitely be said that nitrification bacteria will die faster without ozone than with ozone.
(Aquarientechnik, page 20)