I am following the book "Differential Topology" by Allan Pollack and I am a little bit stuck with transversal intersection between manifolds. I understood the proofs presented in section 5 of such book but still I am not able to fully understan the intuition behind transversality. For example in page 31 the author presents the following figures:
My problem is that I do not know how to determine whether the intersection is transversal or not just from the picture. On the internet I found that if you take one of the manifolds, shake it a little bit and if the intersection is similar or the same then it is transversal. However, I do not know if this is the right approach.
Any thoughts about the intuition behind this property would be greatly appreciated.