Because the amount of money zeros out at the start of each level, people can get confused and think the money doesn't transfer. That's true in terms of meeting the money goal for the level, but it does transfer in terms of being able to purchase upgrades. You'll see the amount that was unused in the previous level is still available for purchasing things.
Links:
[1] http://www.gamezebo.com/admin/content/widgets_assigner/9769