  A horospherical torus about a cusp of a hyperbolic manifold inherits a
Euclidean similarity structure, called a cusp shape. We bound the change in
cusp shape when the hyperbolic structure of the manifold is deformed via cone
deformation preserving the cusp. The bounds are in terms of the change in
structure in a neighborhood of the singular locus alone.
  We then apply this result to provide information on the cusp shape of many
hyperbolic knots, given only a diagram of the knot. Specifically, we show there
is a universal constant C such that if a knot admits a prime, twist reduced
diagram with at least C crossings per twist region, then the length of the
second shortest curve on the cusp torus is bounded. The bound is linear in the
number of twist regions of the diagram.
