How is the Holy Spirit especially associated with the Eucharist?

What is the relation between Eve and the Virgin Mary? By St. Irenaeus (Against Heresies, St. Irenaeus, Volume II, 3:22, pp. 110-111) “According to the divine plan for the salvation of humankind, Mary said, ‘Let it be to me according to your word,’ and thereby obeyed. But Eve did not obey, even though she was still a virgin. Adam was Eve’s husband even while she was a virgin, yet through disobedience, he also became the cause of death for himself, for Eve, and for all humankind. But Mary, who was appointed a husband according to God’s choice and foreknowledge, remained a virgin. By adhering to obedience, she became the cause of salvation for herself and for all humankind. According to the law, a woman betrothed to a man is called his wife even though she remains a virgin. This undoubtedly points to the relationship between Eve and Mary. The events are interconnected and cannot be separated. Eve will not gain her freedom unless the latter (Mary) allows Christ to come from her. Thus, the first became the last, and the last became the first (Matthew 19:30). The prophet also explained this by saying, ‘Instead of your fathers shall be your sons’ (Psalm 45:17). This was fulfilled when the Lord was born, becoming the firstborn from the dead. He embraced the first fathers and brought them into the life of God Himself when He became the beginning of the living human race, whereas Adam became the beginning of the dead human race (1 Corinthians 15:20-22). This is why Luke begins the genealogy with the Lord first, then traces it back to Adam, to affirm that He regenerated these fathers, not that they gave birth to Him into life according to the Gospel. Likewise, Mary’s obedience lifted the curse and disobedience of Eve, for Eve, the first virgin, was bound by her unbelief, and so Mary untied Eve’s bonds by her obedience.” (Against Heresies, St. Irenaeus, Volume II, 3:22, pp. 110-111)