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.
