How to stack nearrow and searrow on top of one another?

Use array. I set the intercolumn space to zero, but surround \nearrow and \searrow with empty subformulas, so the “relation space” is used.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
\setlength{\arraycolsep}{0pt}
\begin{array}{rcl}
&& (b_1,b_2, \dots, b_{l + 1}, \dots, b_{\log N}, l + 1) \\
& {}\nearrow{} \\
(b_1,b_2, \dots, b_{l + 1}, \dots, b_{\log N}, l + 1) \\
& {}\searrow{} \\
&&(b_1,b_2, \dots, \overline{b_{l + 1}}, \dots, b_{\log N}, l + 1)
\end{array}
\end{equation*}

\end{document}

borrowing an idea from henri menke, but rearranging the elements:

\documentclass{article}
\usepackage{amsmath}
\begin{document} 
\begin{equation*}
(b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1)
\mkern 9mu \genfrac{}{}{0pt}{}{\nearrow}{\searrow}
 \begin{aligned}
  & \; (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1)
  \\[.75\baselineskip]
  & \; (b_1,b_2, \dots \overline{b_{l + 1}}, \dots b_{\log N}, l + 1) 
 \end{aligned}
\end{equation*}
\end{document}

Use \genfrac

\documentclass{article}
\usepackage{amsmath}
\begin{document} 
\begin{align*}
&\; (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1) \\
(b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1)
\; \genfrac{}{}{0pt}{}{\nearrow}{\searrow} & \\
&\; (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1) 
\end{align*}
\end{document}

or use tikz-cd

\documentclass{article}
\usepackage{tikz-cd}
\begin{document} 
\begin{tikzcd}
  & (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1) \\
  (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1) \ar[ru] \ar[rd] & \\
  & (b_1,b_2, \dots b_{l + 1}, \dots b_{\log N}, l + 1) \\
\end{tikzcd}
\end{document}