How to properly stack three symbols (e.g. symbols or text above and below convergence arrows or tildes)?

Question

I would like to define a command with three arguments which stacks three symbols or text on top of each other. The \tmb command below does that but creates a bit too much vertical space between the middle and the bottom symbol. The commands \trialone and \trialtwo try to fix that with \raisebox but fail (see below). Then there is a contender based on \mystack, but if the middle symbol is a \to, then it is not vertically aligned with the division bar of a fraction right next to it, for example. Also, there is too little space around the three stacked symbols (to the left and right); see also below.

\documentclass{scrartcl}

\usepackage{amsmath}
\newcommand{\tmb}[3]{\underset{{\scriptscriptstyle #3}}{\overset{{\scriptscriptstyle #1}}{#2}}}% *t*op, *m*iddle, *b*ottom command
\newcommand{\trialone}[3]{\underset{{\scriptscriptstyle\raisebox{2mm}{#3}}}{\overset{{\scriptscriptstyle #1}}{#2}}}
\newcommand{\trialtwo}[3]{\underset{{\raisebox{2mm}{\tiny #3}}}{\overset{\scriptscriptstyle #1}{#2}}}
\newcommand{\mystack}[3]{\substack{#1\\{\textstyle #2}\\[-0.3mm]#3}}

\begin{document}
\begin{itemize}
\item LHS $\tmb{\text{approx.}}{\to}{\text{$n$ large}}$ RHS. Here you see too much vertical space for what's below the arrow.
\item LHS $\tmb{\text{approx.}}{\sim}{\text{$n$ large}}$ RHS. Here you also see too much vertical space for what's below the tilde.
\item LHS $\trialone{\text{approx.}}{\sim}{\text{$n$ large}}$ RHS. Font size not respected.
\item LHS $\trialtwo{\text{approx.}}{\sim}{\text{$n$ large}}$ RHS. Fails if the
  command contains scriptscriptstyle instead of tiny. Still, the raisebox
  command does not seem to work.
\item LHS $\mystack{\text{approx.}}{\sim}{\text{$n$ large}}$ RHS. Looks okay, but the tilde and other middle symbols are not vertically aligned correctly, see
  \begin{align*}
    \frac{A}{B} \mystack{\text{approx.}}{\to}{\text{$n$ large}} \frac{C}{D} \quad\text{versus}\quad \frac{A}{B}\tmb{\text{approx.}}{\to}{\text{$n$ large}} \frac{C}{D}.
  \end{align*}
  We see that the arrow on the left is vertically not aligned with the division bars of the two fractions. Also, there is not sufficient space around the command. None of these problems appears on the right (there is only too much vertical space between the arrow and the ``$n$ large''.
\end{itemize}
\end{document}

Answer 1

The difficult part is to keep the baseline pertaining to the middle symbol. This can be accomplished by typesetting a \vbox for the upper part, where the bottom is a \vtop.

\documentclass{scrartcl}

\usepackage{amsmath}

\makeatletter
\newcommand{\tmb}[3]{%
  \mathrel{%
    \vbox{\offinterlineskip\m@th
      \ialign{%
        \hfil##\hfil\cr
        $\scriptscriptstyle#1\mathstrut$\cr
        \noalign{\vspace{0.3ex}}
        \vtop{%
          \ialign{%
            \hfil##\hfil\cr
            $#2$\cr
            $\scriptscriptstyle#3\mathstrut$\cr
          }%
        }\cr
      }%
    }%
  }%
}
\makeatother

\begin{document}

\[
\frac{X}{2}
\tmb{\text{approx.}}{\to}{n\text{ large}}
\frac{X}{2}
\tmb{\text{approx.}}{\sim}{n\text{ large}}
\frac{X}{2}
\]

\end{document}