So, apparently one can argue that there is a triple reflex of the laryngeals in Latin; I was looking through The Blackwell History of the Latin Language (2007)by James Clackson and Geoffrey Horrocks, and stumbled upon this. I was under the impression that it was only Greek that showed this triple reflex. I shall have to look into this further.
Here are some reflexes which Clackson & Horrocks use to support this conclusion:
*eh1 > Lat. e:, Gk. e:, Skt. a: Ex. *dheh1- > Lat. fe:-ci, Gk. ti-the:-mi
*eh2 > Lat. a:, Gk. a:, Skt. a: Ex. *peh2- 'pasture' > Lat. pa:-sco, Hitt. pahs-
*eh3 > Lat. o:, Gk. o:, Skt. a: Ex. *deh3 'give' > Lat. do:s, Gk. di-do:-mi, Skt. da-da:-mi
However, it seems that this only occurs under certain conditions. For example, when a laryngeal stands on its own between two consonants, it seems to always develop into Lat. 'a'; Greek, naturally, still shows the triple reflex. So, when a laryngeal is next to an 'e' in PIE, the reflexes seem to be the same as in Greek, namely 'e', 'a', and 'o'. Cf:
*h1esti > Lat. est
*h2ent- 'front' > Lat. ante
*h3ekw- 'eye' > Lat. oculus
*sth2to- 'standing, stood' > Lat. status
*dh3to- 'given' > Lat. datus
Quite curious. I wonder why.