Let S be a genus 2 closed surface. Consider the two non-separating red curves (say $\alpha$ & $\beta$) in the picture. I want to construct a pseudo-Anosov homeomorphism $\phi: S \rightarrow S$ with stable foliation $(\mathcal{F}^{s},\mu^{s})$ such that $i(\mathcal{F}^{s},\mu^{s};\alpha)=i(\mathcal{F}^{s},\mu^{s};\beta)$. By Penner's construction of pseudo-Anosov maps, one can construct a pseudo-Anosov map using Dehn multi-twist along two multicurves that are in general position and fill the surface S. In this case, one can see that the stable foliation is supported by a train track symmetric with respect to $\pi$ rotation. But how can one ensure that the intersection number of such a foliation with $\alpha$ and $\beta$ are the same? And if not, how can one construct such a pseudo-Anosov map with the given constraint? Any help will be appreciated.
