Gravitational Time Dilation Scenario

Here's my scenario:

One person with a clock on planet A, one person with a clock on planet B. Planet A's mass is greater than that of planet B.

From what I understand, from each person's point of view, the other planets clock appears to be moving slower (even though one planets mass is greater than the other), correct? And an observer from a 3rd location, say location C, which is very far away from both planets A and B, would see the clock on planet A slower than that of planet B's, correct?

However, imagine the people on planet A and B leave their planets and take there clocks with them. They start to approach a location in between the two planets, but is still ver far away from either planet. As observer A gets closer to observer B, would they see person B's clock getting faster until it got ahead of their own clock? And would person B see person A' clock stay the same or get even slower?

• That depends on who of them actually decelerates. If they just pass by each other, they'll never see anyones clock go faster. I don't see how this isn't just another variation on the twin paradox. Commented Jan 13, 2016 at 14:30
• Are the first two statements I made correct? if both people meet in the middle, as in stop, is what I meant. I apologize if what I'm saying doesn't make any sense Commented Jan 13, 2016 at 14:53