Length contraction

Can length dilation can it happen? Special Relativity do not state length will dilate perpendicular to motion.
However, The alternative theory has length dilation perpendicular to motion.

Consider a disk and a hole that fits the disc exactly both at rest to each other. Then these two objects are slowly parted. Then both are given a velocity and made to move to each other.Then suppose both moves towards each other at velocity v.

Then with respect of the hole the disc will move with velocity v towards the hole. While, with respect of the disc the hole will move at velocity v towards the disc.

If length dilation is correct both will dilate and further there is noway of knowing there is actually any contraction of space.