Transpositions

The Peterson Defense has a very natural feel to it, and as such it's not surprising that there are several transpositional opportunities. Indeed, it's simply the 3 d4 Petrov without white's preliminary 3 Nf3.

Here are some lines that, sooner or later, transpose to other openings:

Petrov 3 d4 (C43)
1. e4 e5 2. d4 Nf6 3. Nf3

Petrov Defense, Modern Variation (C43)
1. e4 e5 2. d4 Nf6 3. Nf3 exd4 4. e5 Ne4 5. Qxd4 d5 6. exd6 Nxd6

Petrov Defense, Symmetrical Variation (C43)
1.e4 e5 2.d4 Nf6 3.Nf3 Nxe4 4.Bd3 d5 5.Nxe5

Philidor Defense, Nimzovich Variation (C41)
1.e4 e5 2.d4 Nf6 3.Nf3 d6

Bishop's Opening, (C24)
1.e4 e5 2.d4 Nf6 3.Bc4

Pirc Defense (B07)
1 e4 e5 2 d4 Nf6 3 Nc3 d6

Center Game, Kupreichik Variation (C22)
1 e4 e5 2 d4 Nf6 3 Nc3 exd4 4 Qxd4 Nc6 5 Qe3 Bb4 6 Bd2 O-O 7 O-O-O Re8 8 Bc4 d6 9 Nh3
(This seems to be a well-worn variation of the Center Game originating in the Romantic era but popping up periodically after that--Winawer beat Steinitz with it in 1896, Tartakower lost with it against Reshevsky in 1937, etc. GM Viktor Kupreichik, however, is a Belarussian player active for the past five decades.)