Oxygen absorbs into the water at the surface and not via bubbles in the water. The bubbles, while pretty, are in the water such a short time that, very little, if any oxygen is absorbed. Yes, fish do like to play in them, but it is not doing a lot for your tanks oxygen intake.
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That doesn't make much sense. The pump supplies a steady stream of air that is being pumped through the water. Each little bubble is coming into direct contact with the water around it just like the water at the surface, more so even because the bubbles have a higher surface area with the benefit of being pressurized (both increase diffusion rates) than the tank's surface area at atmospheric pressure. Yes, each little bubble does not spend much time in the water column but it is a steady stream so oxygen gets added at a faster rate than at the surface. Look up counter current respiration, it is how fish get oxygen through their gills efficiently but the same natural phenomenon of pressure/diffusion gradients applies here also.