  We study semistable extremal threefold neighborhoods following earlier work
of Mori, Koll\'ar, and Prokhorov. We classify possible flips and extend Mori's
algorithm for computing flips of extremal neighborhoods of type k2A to more
general neighborhoods of type k1A. In fact we show that they belong to the same
deformation family as k2A, and we explicitly construct the universal family of
extremal neighborhoods. This construction follows very closely Mori's division
algorithm, which we interpret as a sequence of mutations in the cluster algebra
of rank 2 with general coefficients. We identify, in the versal deformation
space of a cyclic quotient singularity, the locus of deformations such that the
total space admits a (terminal) antiflip. We show that these deformations come
from at most two irreducible components of the versal deformation space. As an
application, we give an algorithm for computing stable one-parameter
degenerations of smooth projective surfaces (under some conditions) and
describe several components of the Koll\'ar-Shepherd-Barron boundary of the
moduli space of smooth canonically polarized surfaces of geometric genus zero.
