When I teach a class on Scripture, one of my favorite exercises is to ask participants to write a nativity play using only one Gospel, pretending it is the only Gospel written.
The Gospel according to Mark: Where's the nativity story? There is none. Mark's Gospel begins with Jesus's public ministry. If we had only Mark's Gospel at our disposal we would know nothing about Jesus's birth and early life.
The Gospel according to Matthew: Jesus is born in Bethlehem. Wise men come from the East asking where the child born king of the Jews is. They observe a star rising. Herod sends them to Bethlehem, where the men find Jesus and offer gifts of gold, frankincense, and myrrh. The men return home by a different route.
The Gospel according to Luke: There is a decree that all must be registered in their own towns. Joseph goes with Mary from Nazareth to Bethlehem. Mary gives birth and wraps Jesus in swaddling clothes and lays him in a manager because there was no room at the inn. There are shepherds in the region watching the flock at night. An angel appears to them and they are terrified. The angels tell them not to be afraid and sing Glory to God. When the angels leave, the shepherds go to Bethlehem. They se the child and tell everyone. People are amazed.
The Gospel according to John: There is no nativity story. In John's Gospel the divine savior comes into the world but Jesus had always been. "In the beginning was the Word, and the Word was with God. He was in the beginning with God."
So ... Some thoughts for you to ponder:
If we had only Matthew's Gospel, it seems that Mary and Joseph lived in Bethlehem. We don't know for sure there were three wise men. We do know there were three gifts given, so we only assume the number of wise men.
If we had only Luke's Gospel, we would know that Mary and Joseph went from Nazareth to Bethlehem, which is approximately 85 miles. There is no mention of a donkey, so did they walk the entire way? How long would that have taken? We assume a stable because of the mention of a manger, but since that is where livestock feed, it could have been in a cave or even outside.
Isn't it interesting to see how we have melded the Gospel stories and added to them?