Homogeneous association

Hi all,

I would like to ask given a three way 2x2x2 contingency table, when any pair of variables is conditionally independent, why there is homogeneous association?

Say given $\theta_{XY(1)}=1$ , why it implies that $\theta_{XY(2)}=1$ as well? $\theta_{XY(k)}$ is the odd ratio given at Z level..