 Failure of transitivity for mixed-frame simultaneity

In units $c=1$, consider spacetime events $O=(0,0)$, $C=(1,2)$ and $D=(1,0)$, with coordinates ordered $(t,x)$. A Lorentz boost of speed $1/2$ assigns $t_O^{\prime }=t_C^{\prime }=0$, while the original inertial frame assigns $t_C=t_D=1$. Nevertheless $O,D$ are timelike separated, so no inertial frame regards them as simultaneous. Hence the relation “simultaneous in at least one inertial frame” is not transitive. This does not contradict transitivity of Minkowski simultaneity relative to an inertial observer for one fixed observer.