Parity mix interferences and pairwise channel cancellation in the attosecond control of electron emission from $H_2^{+}$

We study the single photoionization of simple diatomic molecules such as $H_2^{+}$ by a train of attopulses assisted by a near infrared laser. In particular, we focus on the so called orbital parity mix interferences leading to asymmetrical electron emission. We employ a non-perturbative model obtaining for those asymmetries analytical expressions with a functional form independent of the target structure encoding the interaction of the photoelectron with the laser field to all orders. Related to these interferences, we give conditions at which a pairwise cancellation of channels opened by the laser field occurs. Finally, we exploit the non-perturbative character of our model to analyze the dependence of the asymmetrical electron emission and the angular distribution of photoelectrons with the laser intensity. An asymmetric inhibition of the emission in the classical direction is found. (paper)