Ok First and formost a MAP Gauge measures Manifold Air Pressure (or the pressure of the air entering the engine) hence its name. Not the pressure accross the butterfly.
So when the engine is not running the map gauge reads atmospheric pressure which is about 30".
The butterfly controls the amount of air entering the manifold.
So when you start the engine the pressure drops.
When you put in the carb heat as you said the air is less dense so less enters the engine. This causes the engine rpm to drop which means that it is sucking less air but the butterfly has not moved so the MAP rises.
Now when you are in flight the govenor is controling the butterfly and hence the air pressure in the manifold.
When you raise the colective you increase the blade angle which makes more drag so you need more power. Which means the butterfly opens further so you have more pressure and therefore a higher MAP.
When you lower the colective the oposite happens so less blade angle....... less drag.......... less butterfly opening........... less MAP.
The only thing altitude does is alter the maximum pressure obtainable in the Manifold at the time.
Hope that is clear
