In the Persian form of Mithraism (also referred to as Zoarastrianism); in Persia the priests were called Parsees. Outside of Persia they were known as the Magi. It is from the Magi that we have derived the term magic. In the Roman form of Mithraism; the chief of a Mithraic temple was called father. To be a “father,” the individual had to have risen through all seven stages of Mithraic initiation. The Magi are of historical significance to the history of Christianity. Magi are present in the infancy narrative of Matthew. They give witness to the birth of Jesus. In the Gospels they were presented as wise men, and astronomers; just as the reputation of the Mithraites would have them be. Because the infancy narrative of Matthew is myth, and not an accurate retelling of history, the presence of the Magi in his narrative is not accidental. and is definitely indicative of a sympathetic relationship between early Christians, and first century CE Mithraites.
Why would a sympathetic relationship exist?
Both Christians and Mithraites believe in the immortality of the soul, the reality of personal salvation, the ministry of the angelic host, a God of goodness and light, as well as a final battle with the cosmic forces of darkness, sin, and evil.
In the Roman world, by the first century CE Mithra had taken on the aspect of the incarnate son of Sol. Furthermore, in his exalted state, after the feast made from the “Primal Bull” Mithra is seen as being identical to Sol. Mithra like Christ is seen as being a mediator between Heaven and Earth, responsible for guiding the souls of the elect to paradise. The iconographic similarities explain the sympatico between the two faiths.
Ulansey stated that the worship of Mithra in caves, as it was done among the Romans, was markedly distinct from the Persian form of worship, saying that we cannot explain this as something that occurred by way of a natural syncretic transformation. However, there is a clear path of transformation that can be marked out through the cult of Perseus.
Perseus is the son of the Olympian Zeus and the human Danae. When Zeus impregnates Danae he comes to her in the form of a shower of gold; not in the form of a human being, or other animal (as was often the case with Zeus). The impregnation of Danae is the only scene like this in all of the Greek mythologies. Zeus impregnates Danae in his spirit form; through the use of the ephemeral and symbolic “shower of gold” we are instructed to know that this is the most exalted form Zeus could take. The subsequent birth of Perseus is the closest thing, in all of the Greek mythologies, to a “virgin birth,” a conception narrative analogous to that of Mary, conceiving Jesus by the Holy Spirit.
Danae gives birth to Perseus in an underground cavern. In astronomy the figure of Taurus (the Primal Bull) is the primary symbol of earth. Insofar as Mithra is transformed and exalted through the death and “new-life” of the bull, Mithra is also born of the earth. As a result, the iconographic narratives of the births of both Perseus and Mithra, often depict them as emerging from a rock. And it is not unreasonable to suppose that the underground worship of Mithra served to highlight these features. The earth is the womb wherein we are nurtured, and from which we are born, like Mithra, like Perseus, into new life.
The worship of Mithra in underground caverns had the effect of limiting Mithraic circles to small groups of people. The worship of Mithra is thought to have been exclusively male, though some scholars believe that in some regions women had their own form of Mithraic devotion. In army outposts, at the fringes of the Empire, the worship chambers were often very small, consisting of a narrow room with rows of benches. In urban centers the size and splendor of the temples varied with the demographics of the cities they were in, from simple to ostentatious. However, most worship places were small, and intimate. The intimacy of these temples bears a close similarity to the “house churches” of the early Christians. Many of the Mithraic temples found in Roman cities such as Ostia were later converted to Christian worship.
The last thing that Ulansey points out as being distinct and separate in Roman Mithraism from Persian Mithraism are the seven stages of initiation. I don’t have an easy explanation available to explain this transformation but it may be something as simple as the imposition of a hierarchical social structure natural to the Roman people over the practice of Mithraic worship. There is no reason to say that because this initiatory system exists in the Roman tradition and not in the Persian system we are dealing with two distinct traditions.
 The Origins of the Mithraic Mysteries, by David Ulansey, pg. 34-36