What does this Hose do?

Greetings. While the friends were cleaning the engine of my vehicle, the hose that I showed with the red line below was broken from the beginning. It was very sensitive, nothing flowed through it, but there was a smell of gasoline. It is a very important part of it? There was some people knowing this hose knowing that the hose was not an important thing because the air was passing through it because one end connected to the air filter passes through the hole on the engine. I would be happy if you help ..

The oil steam that is working at the top of the engine with that hose is returned to the intake manifold and burned in the engine. It is connected there to comply with some norms, and not much oil comes from there. It is useful to clean it once in a while. In race cars, an oil filter is attached to the end of that hose and the filtered oil is sent back to the crankcase. You can order it by finding the part code from your chassis number.

thanks koliva.