According to remmert there is a relationship between the crossratios:
C(z,u,v,w) = \frac{(z-v)(u-w)}{(z-w)(u-v)} \text{ and } C(z,v,u,w)= \frac{(z-u)(v-w)}{(z-w)(v-u)} where $z,u,v,w \in \mathbb{C}$
I have tried multiplying things out to see a relationship, but I don't see anything. What could be meant with "relationship"?
Another question deals with the value of the crossratio: On which of the three arcs through $u,v,w$ must z lie so that $0 < C(z,u,v,w) < 1$?
How does one see that there must be three arcs through u,v,w without plotting and how can we characterize the cross ratio without plotting?
Thanks for every suggestion.