\documentclass[tikz,border=5pt]{standalone}
\usepackage[usenames,dvipsnames,x11names]{xcolor}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.pathmorphing,intersections,shapes.arrows}
\usepackage{amsmath,amssymb}
\tikzset{LL/.style={draw=black,decorate,decoration={snake, segment length=3mm, amplitude=1mm,post length=2mm}
}}
\begin{document}
\begin{tikzpicture}
\path[name path=border1] (0,0) to[out=-10,in=150] (6,-2);
\path[name path=border2] (12,1) to[out=150,in=-10] (5.5,3.2);
\path[name path=redline] (0,-0.4) -- (12,1.5);
\path[name path=redlinex] (0,-0.4) -- (10,3);
\path[name intersections={of=border1 and redline,by={a}}];
\path[name intersections={of=border2 and redline,by={b}}];
\shade[left color=gray!10,right color=gray!80] (0,0) to[out=-10,in=150] (6,-2) -- (12,1)to[out=150,in=-10] (5.5,3.7) -- cycle;
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (0,0) to[bend left] (-1,4) to[bend right] (-0.3,3.5);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (-1,4) to[bend right] (6,7) to [bend left] (5.4,3.7);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (6,7) to[bend left] (9,7.5);
\shade [ball color=white] (5,2.5) circle [radius=1cm];
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (5.4,1.5) to[bend right] (8.1,4.6);
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (5,3.5) to[bend right] (7.7,5.1);
\draw[dashed, blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (5,3.5) to[bend right] (5.4,1.5);
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (7.55,4.15) to[bend left] (5.7,3);
\draw [fill opacity=0.3,fill=blue!80!blue] (5,3.5) to[bend right] (5.4,1.5) to[bend right] (8.1,4.5) to[bend left] (7.5,4) to [bend left] (7.7,5) to[bend left] (5,3.5);
\draw [fill opacity=0.3,fill=blue!80!blue] (8.1,4.5) to[bend left] (7.5,4) to [bend left] (7.7,5) to[bend left] (8.1,4.5);
\shade[left color=red!20, right color=red!60] (-0.3,3.5) to[out=-10,in=225] (10,7.5) to[bend right] (9,7.5) to[out=225,in=-10] (1,4);
\shade[left color=red!0, right color=red!50] (b) to[out=172,in=-10] (a) to[out=10,in=150] (b);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt] (-0.3,3.5) to[out=-10,in=225] coordinate[pos=0.27] (aux1) coordinate[pos=0.52] (aux2) coordinate[pos=0.75] (aux3) (10,7.5);
\draw[dashed,red,line width=2.8pt,shorten >= 3pt,shorten <= 3pt] (1,4) to[out=-10,in=225] coordinate[pos=0.1] (auxx1) coordinate[pos=0.6] (auxx2) coordinate[pos=0.9] (auxx3) (9,7.5);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt] (b) to[out=172,in=-10] coordinate[pos=0.8] (bux1) coordinate[pos=0.5] (bux2) coordinate[pos=0.2] (bux3) (a);
\draw[dashed,red,line width=2.8pt,shorten >= 3pt,shorten <= 3pt] (b) to[out=150,in=10] coordinate[pos=0.9] (buxx1) coordinate[pos=0.4] (buxx2) coordinate[pos=0.15] (buxx3) (a);
\foreach \coor in {1,2,3}
\draw[dashed,red,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (auxx\coor)to[bend right] (buxx\coor);
\foreach \coor in {1,2,3}
\draw[dashed,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (aux\coor)to[bend left] (bux\coor);
\shade[left color=black!0, right color=black!80] (a) to[out=-10,in=150] (6,-2) -- (12,1)to[out=150,in=-10] (b) to[out=172,in=-10] (a);
\draw [fill opacity=0.2,fill=red!80!red] (b) to[out=172,in=-10] (a) to[bend left] (-0.3,3.5) to[out=-10,in=225] (10,7.5) to[bend left] (b);
\draw [fill opacity=0.2,fill=red!80!red] (b) to[out=150,in=10] (a) to[bend left] (1,4) to[out=-10,in=225] (9,7.5) to[bend left] (b);
\shade [ball color=white] (7,0.5) circle [radius=1cm];
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (7.4,-0.4) to[bend left] (12.1,1);
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (6.7,1.35) to[bend left] (12.1,2);
\draw[dashed, blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (7.4,-0.4) to[bend left] (6.7,1.35);
\draw[blue ,line width=1.8pt,shorten >= 3pt,shorten <= 3pt] (11.9,1.5) to[bend right] (7.9,0.5);
\draw [fill opacity=0.3,fill=blue!80!blue] (7.4,-0.4) to[bend left] (6.7,1.35) to[bend left] (12,2) to[bend right] (11.8,1.5) to[bend right] (12,1) to[bend right] (7.4,-0.4);
\draw [fill opacity=0.3,fill=blue!80!blue] (12,2) to[bend right] (11.8,1.5) to[bend right] (12,1) to[bend right] (12,2);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (-0.3,3.5) to[bend right] (7,4);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (6,-2) to[bend left] (7,4);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (7,4) to[bend right] (11.5,6.5);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (12,1) to[bend right] (11.5,6.5);
\draw[dashed,line width=2.8pt,shorten >= 3pt,shorten <= 3pt, opacity=0.3] (11.5,6.5) to[bend right] (10,7.5);
\node[rotate=20] at (4.5,0.4) {\color{red}{$S_2\backslash S_1$}};
\node[rotate=30] at (7.7,0.8) {\color{green}{$\pi^{-1}\left(T_{\overline{U},\hat{\varphi}}\right)$}};
\node[rotate=30] at (5.5,2.5) {\color{green}{$T_{\overline{U},\hat{\varphi}}$}};
\end{tikzpicture}
\end{document}