Take a look at this following paragraph that i wrote in another thread

"think of two rockets moving at each other under inertia at a course so that they pass very close. Observer A will look at both clocks when the rockets pass. he will see his own as being T and he will see observer B,s clock as being .5T ..........Observer B will see his clock as being T and he will see Observer A's clock as being .5T ... That being said.. if both rockets accelerate the same amount so as to come to rest beside each other, during the acceleration each will see the others clock run faster than his own and at the point they come to rest both clocks should read the same time."

It seem that this would be true because they both underwent the same events. If its NOT true then both observers would look at observer A's clock and argue where the minute hand is, one would see it on one place and one would see it in another.

IF IT IS TRUE:

then the amount of distance the rockets are apart when they sync their clocks, will greatly affect the amount the opposite observers clock would have to speed up during the "acceleration to rest" in order to make the clocks back in sync upon coming to rest with each other.

A and B are initially stationary. A starting device is placed between them. They both agree when they see the flash from the device to set their own clocks to zero and move towards each other at the same velocity. They will each SEE the others clock to be running faster than their own clock but they will each calculate the others clck to running slower than their own clock, when light travel time is taken into account. When they pass each other A will SEE the same elapsed time on his own clock and on B's clock and vice versa. When they accelerate to a stop nothing special happens because they had the same elapsed time as each other before and after they accelerate to a stop. Before they stop they calculate that each others clocks to be running slower by a amount that is determined by their relative velocities. Obviously when they stop they will notice that their clocks are running at the same rate. The clock rates are completely independent of the distance they were apart when they synchronised clocks and depends only on their instantaneous velocities. You seem to be getting confused between what they SEE and what they calculate and between cumulative elapsed times and instantaneous clock rates.

Fredrik
Staff Emeritus