This is what I need:
Here is what I've just ended up with:
\documentclass[border = 2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{automata,positioning,fit}
\begin{document}
\begin{tikzpicture}
\node[] (B) at (0,1) {B};
\node[state, initial text=, initial below, accepting] (initial) {\textbf{0}};
\node[right=of initial.south, yshift=-5mm, xshift=3mm] (B1) {
\begin{tikzpicture}
\node[state] (10) {$b_{10}$};
\node[state] (11) [below=of 10] {$b_{11}$};
\begin{scope}[every node/.style={scale=.7}]
\path[->]
(10) edge [bend right] node {$\beta_{11}$} (11)
(11) edge [bend right] node {$\alpha_{21}$} (10);
\end{scope}
\end{tikzpicture}};
\node[right=of B1, yshift=-0mm] (B2) {
\begin{tikzpicture}
\node[state] (20) {$b_{20}$};
\node[state] (21) [below=of 20] {$b_{21}$};
\begin{scope}[every node/.style={scale=.7}]
\path[->]
(20) edge [bend right] node {$\beta_{21}$} (21)
(21) edge [bend right] node {$\alpha_{22}$} (20);
\end{scope}
\end{tikzpicture}};
\node[draw,dashed,fit=(B1)] {};
\node[draw,dashed,fit=(B2)] {};
\node[draw,fit=(B)(B1)(B2), inner sep=3mm] {};
\end{tikzpicture}
\end{document}
I could not handle the red edges with remember picture as suggested here.
Additionally, [swap] does not work saying:
(21) edge [bend right] node[swap] {$\alpha_{22}$} (20);
Update :
According to @cfr's advice, I designed the sketch with a different approach using savebox/usebox, instead of nested tikzpictures as follows:
\documentclass[border = 2pt]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{automata,positioning,fit}
\newsavebox\BB
\savebox{\BB}{
\begin{tikzpicture}
\node[state] (10) {$b_{10}$};
\node[state] (11) [below=of 10] {$b_{11}$};
\begin{scope}[every node/.style={scale=.7}]
\path[->]
(10) edge [bend right] node {$\beta_{11}$} (11)
(11) edge [bend right] node {$\alpha_{21}$} (10);
\end{scope}
\end{tikzpicture}}
\newsavebox\CC
\savebox{\CC}{
\begin{tikzpicture}
\node[state] (20) {$b_{20}$};
\node[state] (21) [below=of 20] {$b_{21}$};
\begin{scope}[every node/.style={scale=.7}]
\path[->]
(20) edge [bend right] node {$\beta_{21}$} (21)
(21) edge [bend right] node {$\alpha_{22}$} (20);
\end{scope}
\end{tikzpicture}}
\begin{document}
\begin{tikzpicture}
\node[] (B) at (0,1) {B};
\node[state, initial text=, initial below, accepting] (initial) {\textbf{0}};
\node[right=of initial.south, yshift=-5mm, xshift=3mm] (B1) {
\usebox{\BB}};
\node[right=of B1, yshift=-0mm] (B2) {
\usebox{\CC}};
\node[draw,dashed,fit=(B1)] {};
\node[draw,dashed,fit=(B2)] {};
\node[draw,fit=(B)(B1)(B2), inner sep=3mm] {};
\end{tikzpicture}
\end{document}



tikzpictures is not supported and is not expected to work. – cfr Dec 19 '17 at 00:21scopes instead. I think it is easier, but boxes will avoid the problems with nesting, indeed. I'm not sure how wellremember pictureworks in that case, but you can obviously try it. – cfr Dec 19 '17 at 00:41