  We introduce an idea of constructing Lefschetz fibrations of Weinstein
manifolds from Weinstein handle decompositions on them. We prove theorems that
formulate the idea for the cases of cotangent bundles and some plumbings. As a
corollary, we give diffeomorphic families of plumbing spaces. Those
diffeomorphic families contain some plumbing spaces with names. For example,
Milnor fibers of $A_{4k+3}$ and $D_{4k+3}$ singularities are diffeomorphic if
their complex dimension is odd.
