In areas with Wolves, Bear and Mountain Lions, Pyrs are not usually aggressive enough to defend livestock, and frankly, Anatolians aren't sizable and aggressive enough, either.
That all said, be careful when working with protection dogs. They take their jobs seriously. Children should never be the ones handling livestock these dogs take to be "theirs" to protect, and be wary if a dog begins to treat the animals too much like their own.
At the end of the day, you can never be too trusting with guard animals, bulls, horses and so forth. They are animals, and instincts are beyond the scope of what man can train out completely.