In order to burn, fire needs heat, oxygen and fuel. You can find oxygen in the air. If we remove oxygen by sealing the top of the bottle, then it cuts the oxygen within the bottle greatly. Therefore if there is less oxygen, then there is less air. Air pressure is dependent on the air. However, air pressure outside of the bottle is still the same. This is what creates the suction of the egg into the bottle. The outside of the bottle pushes inward toward the inside of the bottle. When the egg is either popped or removed from the bottle, then it returns back to equilibrium.

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