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If the install instructions call for 3" you must run 3" full size (no reductions) through the wall ro the outdoors. I'm sorry but there's no way around this.
You can't extrapolate to a smaller size. The instructions do not list 2" as a venting option. You must follow the manufactuere's install instructions. It is a code requirement. Sorry if my original answer didn't seem "thoughtful" but there is a simple answer to your question. You can't use a 2" vent.