The birds or pigeons in this covenant making (the ברית בין הבתרים) are not cut in two, but why? What is the meaning behind this?
Read Rash"i on Breishit 15:10. In summary (my loose translation) Rash"i says
The nations of the world were compared to rams and bulls, and they were destroyed (symbolism of cutting these animals). Israel was compared to a dove (yonah - Targum Onkelos on 15:9 translates "gozal" as "bar yonah") and Israel will never be destroyed (thus, the birds were not cut.)
Your reference to Vayikra 17:1 is imprecise, but I assume you're referring to the whole paragraph Vayikra 17:1 - 7? This discusses a rule that people must offer animals for sacrifice prior to eating them. I don't see anything mentioned, there, about cutting / not cutting these animals, and, v 3 refers specifically to oxen, goats or sheep - nothing about birds. Are you referring to the correctly intended verses? If not, please edit your question.