  We formulate and prove Cutkosky's Theorem regarding the discontinuity of
Feynman integrals in the massive one-loop case up to the involved intersection
index. This is done by applying the techniques to treat singular integrals
developed in \cite{app-iso}. We write one-loop integrals as an integral of a
holomorphic family of holomorphic forms over a compact cycle. Then, we
determine at which points simple pinches occur and explicitly compute a
representative of the corresponding vanishing sphere. This also yields an
algorithm to compute the Landau surface of a one-loop graph without explicitly
solving the Landau equations. We also discuss the bubble, triangle and box
graph in detail.
