Conjectural trichotomy for bicontact structures supporting Anosov flows

Let $(xi^+,xi^-)$ be a bicontact structure supporting an Anosov flow $X$. The bicontact trichotomy conjecture. Exactly one of the following holds:

1. $xi^+$ is Anosov contact, it admits a Reeb Anosov flow $R^+$ contained in $xi^-$, and $X$ is a positively skew Anosov flow isotopically equivalent to $R^+$;
2. $xi^-$ is Anosov contact, it admits a Reeb Anosov flow $R^-$ contained in $xi^+$, and $X$ is a negatively skew Anosov flow isotopically equivalent to $R^-$;
3. neither $xi^+$ nor $xi^-$ is Anosov contact, and either $X$ is a suspension Anosov flow or $X$ is not $R$-covered.

This conjecture refines the relationship between Anosov contact structures and skew Anosov flows by specifying where an isotopically equivalent Reeb Anosov flow should occur. Proving it would require removing the bitransversality hypothesis from the cited theorem on bitransverse bicontact structures.