Wait wait wait. Be careful. Yes, a lighter flywheel results in less overall rotational mass, and less parasitic drag on your engine. Therefore, ideally, your car will do a 0-60 faster on level ground.
But beware; if your flywheel is too light, you will notice a decrease in torque when going up a steep hill. You will find that you must rev the engine higher to get the same amount of speed traveling uphill, due to the decreased inertia from the lighter flywheel. Depending on the car, engine, and how much weight you shave from the new flywheel, this characteristic will be shown in varying degrees. I'd suggest you find someone else with a Mazda6 that has done the mod (search Mazda forums) and see their results before going ahead. Good luck!