The birds they sang
At the break of day
Start again
I heard them say
Don't dwell on what
Has passed away
Or what is yet to be
Yeah the wars they will
Be fought again
The holy dove
She will be caught again
Bought and sold
And bought again
Leonard Cohen refers to a “the holy dove” in  Hallelujah : “I remember when I moved in you / and the holy dove was moving too”. 
 In the context of the first verse, this may refer to  the dove in the story of Noah’s arc  whose return served as the announcement for the end of the flood and time to “start again”. 
 It could also refer to the Holy Spirit, who descended on Jesus in the form of a dove at his baptism. (Luke 3:21-23) 

Anthem