From the introduction: “The author investigates a flipping contraction \(g: X \rightarrow Y\) from a 4-fold \(X\) with at worst isolated singularities. If \(Y\) has an anti-bicanonical divisor (= bi-elephant) with only rational singularities, then \(g\) carries an inductive structure involving a chain of blow-ups (la torre pendente), and in particular, the flip exists. This naturally contains Reid’s “pagoda” as an anticanonical divisor (= elephant) and its proper transforms.”
There are recent developments due to Andreatta et al., and H. Takagi. Note that the existence of a minimal model for an algebraic variety of dimension \(\geq 4\) is still an open problem and its key part is the existence of flip.