My experience was slightly different, however....
The ammonia, nitrite and nitrate levels do not usually peak simultaneously.
As the ammonia begins to peak, it is ideally consumed by bacteria that form nitrites. This is a transition -- a gradual process. For example, assuming if you were measuring ammonia and nitrite levels every day....
- Day 11 of the cycle might show a higher ammonia reading, and virtually no nitrites.
- Day 12 might show a slightly lower ammonia reading, and a slightly higher nitrite level.
- Day 13 would show a much lower ammonia reading -- but a much higher nitrite level.
Don't worry about my designated of Day 11, 12, and 13 -- every cycle is different, but most follow the same process. Your nitrites will rise because they are consuming ammonia. Eventually, you will reach a point where your ammonia is near zero -- but your nitrites are peaking.
At that point, the last phase will take over: nitrate-forming bacteria begin to consume the nitrites. At that point, nitrites should drop -- and nitrates should (slowly) rise. Note the "slowly": the nitrite-to-nitrate conversion (phase 2 to 3) happens more gradually than the ammonia-to-nitrite conversion (phase 1 to 2).
Once your ammonia and nitrite levels are zero, your cycle is done. Ensure you monitor here everyday -- those need to be zero. Once they are, ensure the nitrates are rising -- but don't let them rise too high.
Long story short (or long)
-- you're fine. IF you should get "stuck" with high nitrites that won't come down (a fairly common issue), search around here and you will find help.
Until they, just respect the overlap and continue doing what you're doing. Good luck!