I've got a question that may sound pretty stupid, but what the heck:
I know that when heading between north and south via east, you fly at odd thousands, and that when heading between south and north via west, you fly at even thousands (in the US and not above FL410).
What happens when you start off heading southwest, but over the course of your route you start heading southeast? Do you have to either climb or descend 1,000 feet? Or does it not really matter?