I'm trying to understand Kahn-Markovic's celebrated <a href="http://arxiv.org/abs/0910.5501">Immersing almost geodesic surfaces in a closed hyperbolic three manifold</a>. There is something probably quite basic which I can't figure out.

We have $M^3= \mathbb{H}^3/\mathcal{G}$ a closed hyperbolic $3$-manifold, where $\mathcal{G}$ is a Kleinian group. Let $\Pi^0$ be a topological pair of pants with cuffs $C_0$, $C_1$, and $C_2$, and let $\rho\colon\thinspace \pi_1(\Pi^0)\to \mathcal{G}\subset PSL(2,\mathbb{C})$ be a faithful representation. Let $\gamma_i$ denote the geodesic in $M$ that represents the conjugacy class of $\rho(C_i)$ in $\mathcal{G}$ for $i=0,1,2$ (these become cuffs for pairs of pants which Kahn-Markovic construct inside $M$ and glue together to form an immersed almost geodesic surface). 

<blockquote>
<b>Question</b>: Why are $\gamma_0$, $\gamma_1$, and $\gamma_2$ disjoint?</blockquote>

It is essential to the construction that the cuffs indeed be disjoint, because if they intersect, reduced complex Fenchel-Nielsen coordinates don't exist (there is no "foot"). In fact, Kahn and Markovic need many pairs of pants inside $M$ to coexist, so not understanding why the cuffs are non-intersecting even for a single pair of pants is particularly frustrating.