It is an idiom that a crane flies into the sky.

There is no idiom about cranes flying in the sky. The idioms containing the sky are as follows:

The basin faces the sky and the bowl faces the ground, describing the disorder in the family.

Enthusiasm describes the enthusiastic mood and high atmosphere of mass activities, like a raging flame burning according to the sky.

Four feet in the air: of limbs. Describe a fall on your back. It is also a metaphor for lying down and not doing it.

Once every emperor and courtier refers to one person coming to power, the following staff will be replaced by another group.

Heads up, heads up, heads up. Describe arrogance.

The argot that feet die in the air.

Lie face up or back.