  We demonstrate that $\mathbb{Z}_2$ gauge transformations and lattice
deformations in Kitaev's honeycomb lattice model can have the same description
in the continuum limit of the model in terms of chiral gauge fields. The chiral
gauge fields are coupled to the Majorana fermions that satisfy the Dirac
dispersion relation in the non-Abelian sector of the model. For particular
values, the effective chiral gauge field becomes equivalent to the
$\mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to
lattice deformations. Motivated by this equivalence, we consider
Majorana-bounding $\pi$ vortices and Majorana-bounding lattice twists and
demonstrate that they are adiabatically connected to each other. This
equivalence opens the possibility for novel encoding of Majorana-bounding
defects that might be easier to realise in experiments.
