The first time Sasuke registers a crow was the one circling over him in the forest of death after he had lost control. He gazes at Sakura's freshly shorn hair and then up to the sky after he notices a shadow circling above him. No one else is bothered by the birds' presence with the abundance of wildlife around them in the forest. Sasuke is hyper aware of it until nightfall and his team sets out to find shelter for the night.
The next instance was after his first battle with Naruto. As he walked in the downpour towards his future as an avenger he noticed a familiar caw sounding in the distance. It sounded as if it was chastising him for his decisions. He pushed his feet harder to move away from his bonds, his home village, as well as the nonsensical cawing.
After seeing Itachi die in front of him. After learning the truth about Itachi, the Uchiha, and Konohagakure he became filled with rage. A rage so palpable had no capacity to feel any other emotion. His brother had given his life for a village who used him for their own agenda. Burning the village down wouldn't be enough in that moment of white hot rage. After killing Danzo and his untimely reunion with Team 7, he was at an all time low.
Before Itachi's reanimated corpse comes into view he sees a crow and a hawk flying in the same vicinity over the trees he is traveling through. He begins to feel an emotion he has not felt in years, fondness.
After Itachi and Sasuke's final battle together, after meeting with the reanimated Hokage's with the help of his old teacher, he begins to finally come to his own conclusions about the world. As Sasuke races towards the battlefield to help aid in the war he notices a presence flying behind him, this is the first time he has seen the bird behind him rather than above or ahead of him. The crows once were a marker of pain and terror for him, now he felt as though they had been guiding him just as his late brother had tried to.
As Sasuke lays in the valley of the end, his left arm now gone and bleeding out, he notices a crow and a hawk flying overhead. I see now brother, finally.
When Sasuke goes on his journey of redemption he makes note of the times he sees crows. After a trying day of traveling, after helping a village gather supplies or crops, after aiding in the building of a town's structure, he would see or hear the familiar creature in the distance. He feels reassured he is doing something right, he is making amends with the world and within himself.
The first day he brings Sakura along after his journey of redemption he notices a flock of them flying out towards the route they had chosen. The day they find out Sakura is pregnant he notes a birds nest on a branch outside the window of the small clinic they visited to confirm Sakura was with child. The day before Sarada is born Sakura tells him of the dream she had with a black bird circling her the night before. He made sure to watch her carefully that day. The day they arrive back in Konoha from their travels with their few months old daughter he sees one fly alongside them, protecting them like he would.
He feels a connection to the crows different from those of his hawks and snake summons. The instances he has noticed the crows in his lifetime he had been going through different trials and errors. He feels secure now, knowing he has them watching out for him while he protects the people he loves.