The little pipe from the manifold is supposed to channel warm air from the manifold into the engine to help it warm up on cold days. It is, of course, completely ineffective (as you won't get much warm air until the engine is hot - and by that time it's unnecessary) and you can safely junk it. My old 903cc Uno had a similar thing and that also made sod-all difference to the running of the engine.
I put a K&N on my 55SX in the summer, and it starts, runs and warms up as well as it did with the standard airbox and daft pipe on it, even when it's well below zero outside.
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Fart In A Tin
<font color="orange">1994 Punto 55SX, metallic red with black bumpers, 3-door, small, Italian and beautiful! </font id="orange">