  This paper is the sequel to the previous paper [Ne15], which showed that
sufficient regularity exists to define cylindrical contact homology in
dimension three for nondegenerate dynamically separated contact forms, a
subclass of dynamically convex contact forms. The Reeb orbits of these
so-called dynamically separated contact forms satisfy a uniform growth
condition on their Conley-Zehnder indices with respect to a free homotopy
class; see Definition 1.7. {Given a contact form which is dynamically separated
up to large action, we demonstrate a filtration by action on the chain complex
and show how to obtain the desired cylindrical contact homology by taking
direct limits.} We give a direct proof of invariance of cylindrical contact
homology within the class of dynamically separated contact forms, {and
elucidate the independence of the filtered cylindrical contact homology with
respect to the choice of the dynamically separated contact form and almost
complex structure.} We also show that these regularity results are compatible
with geometric methods of computing cylindrical contact homology of
prequantization bundles, proving a conjecture of Eliashberg [El07] in dimension
three.
