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Episode Three begins with Keiichi explaining to himself the events of the night before when we last saw the couple, which was completely new material not found in the manga. In the manga, Keiichi and Belldandy find the temple on the very first night Belldandy arrives, as in the OVA. The new anime also gives a new situation as to how Keiichi and Belldandy get to the temple.
In the manga, Belldandy fell asleep after using a lot of her power (changing clothes, which she didn't do blatantly in front of other people, as well as other things such as reformatting a teapot), and Keiichi fell asleep underneath the temple's steps. The priest then put them in a room to sleep in.
In the OVA, Belldandy simply uses her powers to tell Keiichi where to go, and the temple was abandoned. This is the only incarnation where Belldandy knows where to go, and it's been debated if she really did plan out her whole meeting with Keiichi or not (Belldandy is seen with a magic sphere in Heaven at the beginning of the OVA where the temple can be clearly seen).
As in the manga, the priest is suspicious of Belldandy. However, one major change is the early introduction of the angels, which are only introduced in the Fourth Goddess arc in the manga. Originally in the OVA, Belldandy chants a spell to restore the temple, where here in the anime she is seen by the priest singing the temple back to restoration with Holy Bell. In the manga, though, Belldandy does not use magic of any sort when cleaning up the temple, except for the time when she saved Keiichi from falling.
Speaking of which, in the anime Keiichi succeeds in falling down, although Belldandy uses leaves to break his fall. In the manga, Belldandy uses the roof tiles to stop Keiichi.
As in the manga, the priest leaves since Belldandy has shown superior "spiritual" skills. Thus ends chapter 03 in the manga.