Relativity Theory - in the style of "Fox in sox"

Both observers have identical measuring equipment: Two meter bars, one for the direction of movement (x), one for the orthogonal direction (y), a kilogram, and a clock.

A thinks B's clock is slow B thinks A's clock is slow
A thinks B's meter (x) is short B thinks A's meter (x) is short
A thinks B's meter (y) is correct B thinks A's meter(y) is correct

The observers move with relative velocity v in the x direction. They observe each other, noting the Time Dilation and the Length Contraction (in the direction of movement) In the picture below, a spring gives a momentary tug to both kilograms. The observers measure the resulting velocities, v_A and v_B in the y-direction

A measures v_A B measures v_B
A sees B´s measurement of v_B B sees A's measurement of v_A
Both observers find v_A = v_B

However:

A thinks B's clock is slow		B thinks A's clock is slow
A thinks v_B < v_A		B thinks v_A < v_B
Both observers know p_A = -p_B mv_A = -mv_B Thus:
A thinks B's kg is heavy		B thinks A's kg is heavy
By how much? (1 -v² / c² ) ^1/2 ! (What else?)

http://fy.chalmers.se/~f3aamp/VVV/foxrel.html
Ann-Marie Pendrill, Fysik, GU / CTH, 1997-06-03, revised 1999-10-01
The pictures are taken from Rogers "Physics for the Inquiring Mind". The text is inspired by the tongue-twisting book "Fox in Sox" by Dr Seuss.

A thinks B's clock is slow		B thinks A's clock is slow
A thinks B's meter (x) is short		B thinks A's meter (x) is short
A thinks B's meter (y) is correct		B thinks A's meter(y) is correct

A measures v_A		B measures v_B
A sees B´s measurement of v_B		B sees A's measurement of v_A
Both observers find v_A = v_B