Reception-event dependence of intergalactic redshift ($1+z_{BA}=a(t_A)/a(t_B)$)

A cosmological redshift relates a particular emission event to a particular reception event along a null geodesic. Two sources' redshifts on Earth's past light cone do not specify the light exchanged between those sources. If a photon from B passes through A before reaching Earth, and A's comparison emission lies at that passage event, then $1+z_{BA}=(1+z_B)/(1+z_A)$. Without this causal and temporal specification the ratio need not give the redshift measured in A.