"In those same days, Mary arose and set out in haste..." Or more literally: "Mary, having arisen in those days, went...". Mary arose, she was lifted up by the grace of God within her: she rose to an even higher level of self-giving and generosity and ran to help her elderly cousin. Her assumption, her being taken to higher and higher heights of love, was already at work in her.
Mary's assumption continued in her Magnificathumbling herself, God exalted her. And then she was elevated to new heights of love by the three months she spent caring for Elizabeth.
Satan drags from heaven to earth: "and its tail swept away a third of the stars of heaven and cast them to the earth.". Mary, full of grace and fully open to grace, is elevated from earth to Heaven. Scripture gives us a glimpse of Mary's glory in Heaven: "The sanctuary of God was opened in heaven... A great sign appeared in heaven.". The way Mary is represented shows her as the summit, the crown of creation, the fullest expression of its glory: "A woman clothed with the sun, and the moon under her feet, and a crown of twelve stars upon her head.".
The Christian life is a gradual ascent to Heaven, or rather, an assumption, because God takes us there by his grace. Unlike Christ, who is God, we do not have the power to ascend, to take ourselves there. Mary's humility - there was no weight of pride in her - made it easier for God to bring her to himself. Faith, humility and loving service, inspired in us by the Holy Spirit, are the "winds" in which He carries us.
But as Mary on earth, and as part of the Church (the woman of the Apocalypse is both Mary and the Church), we suffer the constant attacks of Satan, who wants to devour us. "And the dragon stood before the woman which was ready to be delivered, that he might devour her child when she brought it forth." (the new life is a form of assumption, of humanity's constant overcoming of death: that is why Satan desperately opposes it).
The woman was given "the two wings of the great eagle". -another suggestion of assumption, of being taken higher-to escape the serpent. The serpent acts on earth; the eagle-spirit carries us to the heights of Heaven. With Mary, in her arms or in the tail of her cosmic garments, we too are carried to God. And in the resurrection of the flesh, we too will enjoy our own "assumption," not on Mary's level, but glorious all the same.