"Blow through" can also mean to pass through a place briefly. Example: I plan to blow through Bath on my way to London.

"Blow through" literally means "blow air through". For example, "If you hold a drinking straw up to your lips, you can blow through it." or "The wind blew through the door." There are a few figurative meanings. You can say that a storm "blew through" an place. This is the same as saying the storm "passed through" or "went through" an place. It can also mean "break through", as in "A bullet blew through the wall," or "An explosion blew through the building." Finally, it can mean "to do something quickly", like "He really blew through the test!" or "Don't just blow through your reading, make sure you understand it."