One of the more intriguing depictions of today’s feast is here by the American-born artist Brigid Marlin.
Most parishes will probably stop at the first reading from Zechariah and not consider the option from Saint Paul, which reads in part:
Brothers and sisters:
Let love be sincere;
hate what is evil,
hold on to what is good;
love one another with mutual affection;
anticipate one another in showing honor. (Romans 12:9-10)
It’s a curious thing that part of this reading is also an option for the Wedding Lectionary. What are the commonalities in the relationship between Elizabeth and Mary and married spouses?
Some spouses I know are competitive. Limited to the realm of fun and games, perhaps this is a good thing. But there may be a better way, outside of sporting considerations.
Mary, thought to be an adolescent in Luke 1, goes out of her way to visit her older cousin and offer service to her. Mary anticipates, and the question for husbands and wives with respect to the other, do we anticipate needs, see them ahead of time? The hill country of Judea (Cf. Luke 1:39), imaged above, does not always allow one to see what is ahead. Unlike the open ocean or the wide stretches of farms on plains. Caring for the beloved, do we think to look ahead, to scout beyond the next hill or peek into some hidden valley? Are we seeking potential opportunities? Avoiding dangers before they surface?
Catholic Sensibility 
I’ve had a somewhat different take on the visit. Mary, filled with grace and now with the very presence of Godhead, is moved to urgently (haste) generous action.
But the trip to visit Elizabeth had to be done with family blessing and arrangements – a teenage girl in that culture was not travelling on her own between Galilee and Judea. It could not have been covert.
That said, Elizabeth’s welcome would have opened up the door for Mary to talk with Elizabeth and Zechariah – about the angelic message and what it portended, for her as a woman and as a Jew.
Zechariah was, after all, a priest in the Temple, and would have been deeply immersed in trying to understand what his wife’s and Mary’s pregnancies *meant* – and to help them (while he couldn’t talk, he could *write* though literacy among Jews in that era wasn’t as widespread as it became in later eras).
While Scripture offers no details, it’s not far-fetched to speculate that Mary likely received not only priestly blessings and education from Zechariah, but also some important training about the process of childbirth and motherhood – things that Elizabeth had long wanted to experience in the first person and was finally able to do (as childlessness had likely held as a sign against her and Zechariah). My point is, as good as Mary gave, she likely also received in turn, to fortify her for her own journey to new motherhood.
Further speculation: perhaps Zechariah was the one who told Simeon and Anna to persevere a bit longer, that the promise of their hopes would soon be coming to the Temple, so that Simeon and Anna were ready and on the lookout, as it were. Zechariah might even have tipped Mary off to look for Simeon when the time came to present Jesus at the Temple.
PS: As in the tradition of the Hebrew Scriptures, it is the mother of the King who is chief Queen*, the Magnificat can be seen as fulfilled in Mary’s taking her place at the side of her Son. Today used to be the feast of the Crowning of the BVM – an observance that has been moved to what used to be the octave of the Assumption (while the Visitation used to be observed on the first day after the octave of the Nativity of St John the Baptist).
* A feature not unique to the court of the Davidic line; it’s also a feature of some other cultures, as it was for a while in the imperial Japanese court and the court of the Ottoman sultans after Suleiman into the 18th century.