This is such a trivial question that I hesitated to ask it, but I can't find the words to search for it online so here it goes.
I think we are all familiar with rewriting equations and putting each step on a new line like this: $$\begin{align} (x + y)^2&= (x + y)(x + y)\\ &= x^2 + 2xy + y^2 \end{align}$$
To save some ink, you omit the LHS if it doesn't change from step to step. Here, there are only equalities, so it is not necessary to distinguish between the equality of $(x + y)^2$ and $x^2 + 2xy + y^2$, or $(x + y)(x + y)$ and $x^2 + 2xy + y^2$. But how does this work with inequalities?
Take this example: $$ \begin{align} z &> (x + y)^2\\ &> x^2 + 2xy + y^2 \end{align} $$
Is this the correct way to write this down? Or does this incorrectly imply that $(x + y)^2 > x^2 + 2xy + y^2$ and should the second line have an equals sign?. Essentially, I'm asking if the equality sign refers to the LHS or to the previous line? Of course, confusion can be avoided by not omitting the LHS, but with longer equations this can become very tedious.
When chaining signs, each sign will show the relationship between its previous (not the first) and next side. So, correct would be:
\begin{align} z &> (x + y)^2\\ &= x^2 + 2xy + y^2 \end{align}
Note that this is also true for other signs, not only $<>$. For example, both
$$1\neq 2\neq 3$$
$$1\neq 2\neq 1$$
are correct and accepted. If we want to say three numbers are distinct two by two, we should write:
$$1\neq 2\neq 3\neq 1$$