Whenever I do yoga or other excercies, I often get vertigo and blurry vision (close to a very short blackout) between movements. Is this normal?

Exam needed. Vertigo and blurry vision occurs for a variety of reasons - some of which are very serious. If you get this with a variety of exercises you need to see a physician. This may progress and happen when driving.
Not normal. This is not normal and i would go see your regular doctor for further evaluation of this issue. Many issues such as low blood pressure, irregular heartbeat, inner ear problems can cause issues like your description.