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Hydrogen peroxide can oxidize contaminates in the water when kept at an appropriate concentration, but needs to be paired with another chemical to sanitize the water. In theory it can be kept at a high enough concentration in the water as to provide oxidation and sanitation, but at that level the water would be extremely unpleasant to skin and eyes and probably not good for plaster or anything else the water touches.
As this type of pool has no benefits over a chlorine pool but subject to far more downsides, TFP does not promote nor recommend attempting to maintain a pool in such a manner.