The larger diameter pipe that runs back under the car is connected to the top of the fuel tank. Whenever fuel is used out of the tank air needs to be let back in to replace the fuel so it is sucked in through there. When you remove the filter its best to either connect that hose to the little black filter on the chassis leg or fit a small breather filter to it for a belt and braces job.
Leaving it open runs the risk of dirt getting sucked into the fuel system, even a piece of rag cable tied around the end of it would be better than nothing.
The small diameter pipe that runs to the filter can be cut right back to the throttle body, bent over and cable tied back on itself to prevent any air leaks getting back into the inlet mani. I am an EP8* man so I cant say for sure what to do on a V mate, sorry.