  A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G
and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic,
if and only if G can be transformed into H by a series of operations called
Whitney switches. In this paper we consider the quantitative question arising
from Whitney's theorem: Given two 2-isomorphic graphs, can we transform one
into another by applying at most k Whitney switches? This problem is already
NP-complete for cycles, and we investigate its parameterized complexity. We
show that the problem admits a kernel of size O(k), and thus, is
fixed-parameter tractable when parameterized by k.
