Superhydrophobic surfaces can dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. When the lubricating layer of gas is kept trapped within the micro-rough texture, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip/no-slip conditions taking into account or not the displacement of the gas/water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated extensively. By means of numerical simulations and global stability analyses, we assess the influence of superhydrophobic surfaces (as well as their modeling) on the laminar-turbulent transition process in a channel flow. Considering modal transition scenarios for isotropic micro-roughnesses, a strong transition delay is found using a spatially-homogeneous slip length or heterogeneous slippery boundaries with flat, rigid liquid/gas interfaces. Whereas, non-isotropic micro-roughnesses, such as riblets inclined with respect to the streamwise direction modeled with a tensorial slip condition, are found to promote the onset of a new type of modal instability bearing some resemblance with crossflow modes developing on swept wings. When the interface dynamics is taken into account, the transition delay effect is reduced with respect to flat slippery surfaces. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimate transition delay. Contrariwise, non-modal transition, triggered by a broadband forcing, is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on their geometrical features, on the interface dynamics, and on the specific physical mechanisms triggered on the considered transition process.