A flip in birational algebraic geometry replaces a small projective birational contraction 
by another small projective birational
morphism 
, reversing the relative sign of an adjoint
divisor. Small means that the exceptional locus contains no prime
divisor. For 
, the negative side has
relatively ample and the positive side
has the transform 
relatively ample.
The elementary version contracts one extremal ray and has relative Picard number one on the negative side. A divisorial contraction instead removes a divisor.
Generalized pairs use 
in place of 
and retain the same nef data on
higher models. Termination concerns the number of consecutive flips and is distinct
from existence of a positive model for a given contraction. A flop preserves the
relative numerical class of the canonical divisor
instead of reversing a strictly negative sign.
