When you push up the balloon, several things can happen depending on the context:
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Volume decrease: In a model of the lungs and diaphragm, pushing up on the diaphragm lowers the volume in the bell jar, increasing the pressure and forcing the air out of the balloons until they collapse. Similarly, when you push up the balloon at the bottom of a bottle, the volume of the bottle decreases, causing the air inside to compress.
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Air displacement: Pushing up on the rubber of a bottle can cause the air inside the bottle to get squashed up, resulting in higher pressure that pushes air out of the bottle. When you punch a hole in a bottle, the air molecules in the bottle have an exit, and they are pushed out as a balloon fills the space inside.
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Deflation: In a model of the lungs, pushing up on the bottom balloon causes the balloons (representing the lungs) to deflate, pushing out the air. Similarly, when you push a balloon inside a plastic bottle and stretch the balloon opening over the bottles top, the balloon will not inflate because the bottle is already filled with air particles with no escape route.
