Don't use hydrogen peroxide in your pool.
No, it’s not a practical pool sanitizer.
Hydrogen peroxide breaks down almost immediately in sunlight and warm water. You’d be dumping gallons of the stuff into the pool every few hours just to keep the bacteria count down. And at the concentrations needed to actually sanitize, it’s corrosive and hazardous to handle. Meanwhile, chlorine or bromine give you lasting protection for a fraction of the cost and hassle.
Pool stores will occasionally sell “alternative” systems that use hydrogen peroxide, but they always involve UV lights or other expensive equipment to keep the peroxide from dissipating. For a typical home pool, stick with the old standards. They work.
Save the peroxide for cuts and scrapes.