Sorry just re read your post and thought of more.
The filter shouldn't be changed or even touched really during a cycle. The point of a cycle is to let the bacteria in the filtration system build up to create what we call good bacteria. Good bacteria changes ammonia to nitrite then nitrate. You'll help the levels get down and keep them down with water changes to be safe for live aquatic animals. Once the cycle completes you should have enough good bacteria to take care of (ammonia and nitrite) the bio load. At this point the only way to lower nitrate levels is by water changes and good tank maintenance. I would recommend after the cycle to do two 25% water changes a week. If you notice its not keeping nitrate levels under control ( as close to 0) then you'll need to raise the % you change out.
There was something I was going to add and I forgot if and when I remember ill re post.