difference equation block diagram delay or advance confusion
It depends from which side of the delay block you look at. Below is an example one sample delay from left to right in the arrow direction :

$$ x[n] \longrightarrow \boxed{ z^{-1} }  \longrightarrow y[n] $$

Then either $y[n] = x[n-1]$ or $x[n] = y[n+1]$ are both correct and equivalent expressions.

The first one is written when you trace the delay block in the arrow direction. And you get a delay effect from input x to output y. This is the normal operation direction. 

The latter expression is obtained when you trace the delay block in the opposite direction of the arrow. Which gives you an advance effect from signal y to signal x.