Generalized Chain Surgeries and Applications

We describe the Stein handlebody diagrams of Milnor fibers of Brieskorn singularities $x^p+y^q+z^r=0$. We also study the natural symplectic operation by exchanging two Stein fillings of the canonical contact structure on the links in the case $p=q=r$, where one of the fillings comes from the minimal resolution and the other is the Milnor fiber. We give two different interpretations of this operation, one as a symplectic sum and the other as a monodromy substitution in a Lefschetz fibration.