shanefish;1493635; said:
Here's a test I did with nitrites. I was setting up a water filtration and cycling system. It was 4 55 gallon plastic drums that I hooked up a 350 gph cannister filter on. After I had the system up and running my nitrites peeked in a few days and stayed there. After a couple weeks of no change I decided to see what would work. I was setting up 3 10 gal aquariums and I used the water from my system, I used the same gravel and airstones in all. The first tank I did nothing to, the second I added a cup of gravel from an aquarium wich had been set up for a while and the third I placed a dirty(really in need of being cleaned) power filter. 24 hours later the first tank no change the second a small change in the right direction but the third with the nasty power filter no nitrites wiped them out in less then 24 hours. So I added a dirty filter cartrage to my water system and it lowerd the nitrites in a couple days and I never had a problem since. The water filter system cycles in a couple days if I use a lot of water out of it.
You moved cycled biomedia from an established system to one that was either not cycled or lacking sufficient biomedia (vague on which). Ok, most of us do this.
I'm, however, skeptical of some of your numbers and information. You can't cycle another tank with water, that is simply NOT possible. You can say you did it all day, it didn't happen. Your biological bacteria aren't floating around in your water column. If they are they're not alive anymore

I've even tested this myself repeatedly. Moving water from one tank to another had no effect on cycling time.
On one system you say nitrites showed up in a few days, but you don't specify whether you were setting this system up from scratch or you'd already added cycled media or something like biospira. Setting up a fresh tank you don't get nitrites within a few days.
As far as the nitrites peaking and staying there for several weeks you probably didn't have sufficient surface area for bacteria to grow, which is why adding more biomedia helped, on top of the fact that that biomedia was already seeded with bacteria.
Biological bacteria takes a certain amount of surface area to grow on, so if you lack that surface area (which is what the media provides) you will not grow a sufficient number to fully cycle.
This is why companies sell specific biomedias, they are manufactured to have an extensive surface area. Ceramic rings, biochem stars, bioballs, all those type of things are meant to provide plenty of surface area for your biological bacteria to grow on. Household items like plastic pot scrubbers can also provide that. Add as much as possible and you won't usually have those problems.