We investigate theoretically and numerically the inverse energy cascade in statistically steady two-dimensional turbulence. We perform a numerical testing of the analytical results proposed by Lindborg (J. Fluid Mech. vol. 338, 1999, p. 259), and we show that these predictions are quantitatively verified in the inverse energy cascade provided that the quantities involved in the spatial average computation are also averaged over all directions. Then, we define a simple measurable criterion based on the kinetic energy induced by coherent vortices in physical space. Using this criterion, we introduce more selective analyses of the energy cascade that reveal spatial properties of energy transfers which are concealed by global spatial averages. We conclude that there exist convective fluxes in both physical and scale space that feed the energy cascade processes in strongly energetic regions. In two dimensions, these regions are mostly localized around coherent structures. In the turbulent background, this mechanism manifests itself as a deficit of the kinetic energy and weaker inverse energy transfers.