What are the correct equilibrium arrows?
According to IUPAC: Quantities, Units and Symbols in Physical Chemistry (Green Book), the arrows are used differently for composite mechanisms in chemical kinetics.

In case of a simple mechanism that is composed of a forward and a reverse elementary reaction (i.e. reactions that occur at the molecular level in one step), it is conventional to write these in one line using two double-sided arrows $(\rightleftarrows)$.
For example:

$$\begin{align}
\mathrm{A} &amp;\to \mathrm{B + C}\\
\mathrm{B + C} &amp;\to \mathrm{A}\\
\hline
\mathrm{A} &amp;\rightleftarrows \mathrm{B + C}
\end{align}$$

This is distinguished from a net reaction, which is written with two one-sided arrows $(\rightleftharpoons)$.
For example:

$$\begin{align}
\mathrm{A} &amp;\rightleftarrows \mathrm{B + C}\\
\mathrm{B + C} &amp;\rightleftarrows \mathrm{D + E}\\
\hline
\mathrm{A} &amp;\rightleftharpoons \mathrm{D + E}
\end{align}$$

The two-sided arrow $(\leftrightarrow)$, which indicates resonance structures, shall not be used for reactions. 

I guess that every elementary reaction that is proceeding in both directions $(\mathrm{A} \rightleftarrows \mathrm{B + C})$ may also be considered a net equilibrium reaction $(\mathrm{A} \rightleftharpoons \mathrm{B + C})$, but not every net equilibrium reaction $(\mathrm{A} \rightleftharpoons \mathrm{D + E})$ is an elementary reaction that occurs at the molecular level in one step $(\mathrm{A} \rightleftarrows \mathrm{D + E})$. Therefore, I assume that one-sided arrows $(\rightleftharpoons)$ may be used for all equilibrium reactions, whereas double-sided arrows $(\rightleftarrows)$ could be wrong when one combines composite mechanisms to obtain net reactions.