TITLE: Kirby calculus on Mazur manifolds
QUESTION [10 upvotes]: I have questions about Akbulut and Kirby's paper Mazur manifolds.
I couldn't figure out the following equality passages:


Any help will be appreciated.

REPLY [9 votes]: Here is a proof with pictures. Observe that blowing up and blowing own doesn't change the 3 manifold,i.e, the boundary. So all these above pictures  have same boundary. As a 3 manifolds all of these are isomorphic.