What is the best way to intuitively and visually distinguish between immersion and submersions? For example, I understand that the standard picture of the Klein Bottle in R^3 is an immersion. How do I see this? (Obviously, it's not an embedding because the Klein Bottle self-intersects in R^3. But how do I see that the differential map is 1-to-1 but not onto?) What would a submersion look like? Also, can I visualize a copy of the real line in R^3 so that, it is an immersion but not a submersion nor an embedding? Also as a submersion but not an immersion?