I'm glad both of you are really enjoying your new aquatic lives. It is a hobby that my dad, brother and I are hooked on and will never give up.
As for cycling , a complete cycle will probably take about 2-3 weeks but the water and filter should be safe for fish after about a week. Remember that once fish are in the water you must do water changes frequently, about ever third day for the 29g and every second day for the 10g. And make sure to be using dechlorinator if using tap water.
Are either of your tanks planted?
And as a betta owner (x4) I am curious to know how your betta is handling being in a tank with your catfish, being an aggressive, territorial fish (females not as much as males, however).
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