Why was the invasion of italy important in the allied war effort

It was important for couple reasons;

1. In theory, opened a second front the Germans had to deal with. This was something the Russians had been demanding for a while. Unfortunately, Europe turned out to be quite tough to get through and did not divert as much as German troops as was hoped, and

2. Another important effect was the extra experience it gave allied forces in the amphibious warfare and fighting the Germans in general. 

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