Certainly part of what Ovid is thinking about is the act of translation, of "carrying over" something from one place, one tongue, one mind, to another. This is not a simple matter -- in fact, to this day no one has quite figured how translation happens. It's enigmatic in part because it involves something that we consider to be "the same," i.e., sense, or meaning, taking on the clothing of a new language, which inhabits its own world of meanings. Every translator knows that when meaning is ported from one tongue to another, it takes on new accents, new inflections. So something that is "the same" is not the same. The new tongue aspires to reflect the original, but can only do so within its own very different signifying structures, forms and meanings. Something is perhaps lost, perhaps something is gained, and continuity is problematic.
How this occurs is a mystery.
For Ovid, the burden of transmitting a tradition, a cultural Weltanschauung (worldview) in all its richness, is what poets are supposed to do. Of course another word for translation, in which A undergoes a journey in which it both remains A and yet becomes new and other than A -- is metamorphosis. We note that when Ovid introduces Arethusa, he calls her by a new name, using a Latin word that appears only here*: He calls her Alpheias. Arethusa, who received Diana's help to escape the Greek river Alpheus, is still Arethusa, but has changed. She's been translated.
Ovid explores metamorphosis across the entire imaginative spectrum. In terms of the structure of the poem, the first five books are in some sense about the Westward movement of Greek mind, Greek culture, Greek worldview from its early origins in Thebes and Mycenae to its new rooting in southern Italy.
One telltale sign that these five books can be taken as one block of the edifice: Book 6 begins with Athena moving eastward to Lycia. Other characters in Book 6 will also be from areas of Anatolia, including Phrygia, the home of Tantalos, father of Pelops (who gave his name to the Peloponnese) and Niobe. (A quick overview of the 15 books of the poem can be found here.)
The latter portion of Book 6 moves North to Thrace and ends with Boreas, the North Wind. In book 7, Jason and Medea take us all the way to Colchis, on the eastern coast of the Black Sea. The birthplace of Medea is even farther East, in what is now Georgia, some 2,500 miles from Greece overland, according to Google Maps:
This geographic outwardness will continue in Books 8 and 9, which largely occur to the South, in Crete. Obviously it's too soon to say anything for sure, but let's hypothesize that Ovid is weaving his tales in a kind of circle. No matter how far we go, the matter always relates back to the core of Greek culture.
But if Ovid is shaping a circle in space -- and this might well be too simple a formulation -- his tales are also moving through time. The last five books of the poem bring us forward to the Trojan war -- we follow the seeds of the that conflict, the fates of Achilles and Agamemnon, and then it's westward again with Aeneas, Romulus, Pythagoras, the voyage of Aesculapius, and the apotheosis of Julius Caesar. By the end, Ovid's poem, and the traditions it traces, have become his day, his city, his poem. The core of Greek culture has shifted to the West, following the trajectory of the sun.
Only, for reasons that still baffle, the poem no sooner arrives at Rome, the new center of things, than the poet is exiled to Tomis, on the Black Sea, some 2,000 km from the city of the Caesars.
*"The substantive Alpheias is Ovid's invention. It is neither a patronymic nor a geographical term, as its form suggests." - William S. Anderson, Ovid's Metamorphoses, Books 1-5, p. 548.
Turner, Ovid Banished from Rome, 1838