Virgin Mary is constantly present each time the liturgy is celebrated. First of all because as a human being just like us, she worships God as the one and true God. Secondly because she has a particular and unique place in the achievement of the two major mysteries regarding mankind's salvation (the Incarnation and the Redemption), hence in the liturgy celebrating those mysteriesof the Faith. Moreover, the Mother of the Word of God takes up a special place in the Eucharistic liturgy, just as St Augustine reminds us, "Jesus' flesh is Mary's flesh" …
Mary is not the God of the Temple, she is the temple of God
Nevertheless, however special the place taken up by the Holy Virgin within the liturgy of the Church, she is not the core of it—the worship of adoration (latria) should be rendered to God alone: God alone is the first and foremost aim of the liturgy of the Church. As for Mary, she receives from all those who pray to her a worship of veneration (dulia – and even hyperdulia in so far as Mary alone is greater than all the saints and angels put together). But of course—Mary is not the God of the Temple, she is the temple of God…
However, since the very beginning of the Church, and all over the world, the liturgy has been celebrating and honoring the Mother of God, the one who sung in her Magnificat: "... from now onwards all generations will call me blessed"..
A place of honor in the liturgy
Mary features high in all the liturgies of the world (Eucharistic liturgy, Sacramental liturgy, Divine Office). This can be noticed especially in the rites of the Oriental Church, for instance where the Virgin Mary is central in the celebration of Orthodox offices, being honored as Theotokos (Mother of God) all the liturgical year round.
In the universal Church, the liturgical year is marked with four great Marian feasts: the Immaculate Conception, the Annunciation, Mary Mother of God, the Assumption, as well as with many lesser feast days (at least sixteen); not to mention votive masses in the honor of the Virgin Mary. This shows just how important and venerated the Virgin Mary is in the Eastern as well as the Western liturgy of the Church, whatever the culture, and "from generation to generation"...