Identify this Intake Hose

[Albertcado]

Hi All,
Can someone identify exactly what the circled intake hose is called and its main purpose/function?
How do I also check that it's secure and not leaking?

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[IndyRN]

Air intake for PCV system.

Edit: The use is to reroute crankcase gasses and put them back into the combustion chamber. Before all of the emissions stuff, they'd just dump them out of a breather. Now that valve exists to reduce the carbon footprint of the vehicle.