We prove that the arithmetical sum of two Cantor sets whose sum of Hausdorff dimensions is slightly bigger than 1 is generically an M-Cantorval. We conclude that, in most cases, homoclinic bifurcations in a surface associated with non-trivial basic sets with Hausdorff dimension slightly bigger than 1 present hyperbolicity and stable tangencies for positive values of the parameter, both with positive density at the initial bifurcation parameter.