Hi. The cycle in the new tank will depend more on the state of your filters rather than the water you put in it. Personally I would rebuild and fill with conditioned tap water and do a fish less cycle to prove the tank is suitable for fish. When 4ppm ammonia is reduced to zero with zero nitrites in 24 hrs, then do a major
WC to reduce the nitrates that will have been produced and add the fish 24 hours later. If all the test results are good after a week then I would slowly increase stock, but only a few fish at a time. A good liquid test kit (avoid test strips, they are really unreliable) will be your best friend! As I said, that is what I would do but others may have different opinions. Good luck with the new tank.
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