When either the intake manifold or its gasket is faulty, it can lead to a vacuum leak in the engine. This can cause unmetered air to be drawn into the engine, which can lead to a rich fuel mixture.
When this mixture burns, it can create white smoke that is visible from the exhaust pipe. Additionally, a vacuum leak can also cause other issues such as engine stalling, rough idle, and reduced fuel efficiency.
If you suspect a vacuum leak is the cause of your Mazda's white smoke issue, it's important to have the intake manifold and gasket checked by a qualified mechanic.