  Binary systems that host a massive star and a non-accreting pulsar can be
powerful non-thermal emitters. The relativistic pulsar wind and the
non-relativistic stellar outflows interact along the orbit, producing
ultrarelativistic particles that radiate from radio to gamma rays. To properly
characterize the physics of these sources, and better understand their emission
and impact on the environment, careful modelling of the outflow interactions,
spanning a broad range of spatial and temporal scales, is needed. Full
3-dimensional approaches are very computationally expensive, but simpler
approximate approaches, while still realistic at the semi-quantitative level,
are available. We present here the results of calculations done with a quasi
3-dimensional scheme to compute the evolution of the interacting flows in a
region spanning in size up to a thousand times the size of the binary. In
particular, we analyze for the first time the role of different eccentricities
in the large scale evolution of the shocked flows. We find that the higher the
eccentricity, the closer the flows behave like a one-side outflow, which
becomes rather collimated for eccentricity values $\gtrsim 0.75$. The
simulations also unveil that the pulsar and the stellar winds become fully
mixed within the grid for low eccentricity systems, presenting a more
stochastic behavior at large scales than in the highly eccentric systems.
