  Let $\varphi_0$ be a smooth conservative diffeomorphism of a compact surface
$S$ and let $\Lambda_0$ be a mixing horseshoe of $\varphi_0$. Given a smooth
real function $f$ defined in $S$ and a small smooth conservative perturbation
$\varphi$ of $\varphi_0$, let $L_{\varphi, f}$ and $M_{\varphi, f}$ be
respectively the Lagrange and Markov spectra associated to the hyperbolic
continuation $\Lambda(\varphi)$ of the horseshoe $\Lambda_0$ and $f$. We show
that for generic choices of $\varphi$ and $f$, the Hausdorff dimension of the
sets $L_{\varphi, f}\cap (-\infty, t)$ and $M_{\varphi, f}\cap (-\infty, t)$
are equal and determine a continuous function as $t\in \mathbb{R}$ varies;
generalizing then the Cerqueira-Matheus-Moreira theorem to horseshoes with
arbitrary Hausdorff dimension.
