Nazism: Path to higher consciousness is a gradual, step-by-step process--from dullness to spiritual awakening
New Age: Illuminati teaches the step-by-step Eight-fold Path of Enlightenment
Nazism: The symbol of the highest degree of the gradual process was the Eagle, hence the German Eagle.
New Age: The Phoenix Eagle of the Illuminati was the ancient "Bird of Reincarnation". After 400-500 years, the Phoenix Eagle would be consumed by fire into ashes, but the egg it left behind would give birth to a new Phoenix which would arise out of the ashes of the old eagle. (Thus, the threefold cycle of Life/Death/Rebirth would be completed)