joko....complicated topic and I think that a Respiratory Physiologist would be better qualified to deal with the problem.
Firstly, the transfer of oxygen from the lungs to the blood is complex and does not depend upon how much air one has in one's lungs.Also,there is a maximum amount of air that the lungs can take..i,e you just can't keep filling them up with air like a balloon, because like a balloon, they could over inflate and "burst"
Now the oxygen requirements may be reduced (so that you can stay under water longer) by reducing your heart rate (by relaxing) and moving as little as possible.
Training and adaptation to reduced oxygen is also important.
Hyperventilation...panting and increasing your breathing rate is dangerous, as it blows off your carbon dioxide which is very important.