Bend vertical arrow in commutative diagram in Tikz

Question

I would like the double arrow in the center to be bend. Here is what I have now:

\[\begin{tikzcd}
    \bullet \arrow[bend left=75]{rr}[name=O]{ff'}   \arrow[bend right=75]{rr}[name=S,swap]{gg'} 
                \arrow[bend left=50]{r}[name=U]{f}          
                \arrow[bend right=50]{r}[name=D,below]{g}
        & \bullet
    \arrow[Rightarrow,to path=(U)  --  (D)]{}   
                \arrow[bend left=50]{r}[name=W]{f'}         
                \arrow[bend right=50]{r}[name=E,below]{g'}
        & \bullet
    \arrow[Rightarrow,to path=(W)  --  (E)]{}
    \arrow[Rightarrow,to path=(O) -- (S)]{}
\end{tikzcd}\]

All my attempts have failed.

Answer 1

Credits to Gonzalo Medina: https://tex.stackexchange.com/a/50955/101651.

\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
Like this?
\[
\begin{tikzcd}
    \bullet \arrow[bend left=75]{rr}[name=O]{ff'} 
            \arrow[bend right=75]{rr}[name=S,swap]{gg'} 
            \arrow[bend left=50]{r}[name=U]{f}          
            \arrow[bend right=50]{r}[name=D,below]{g}
    & 
    \bullet \arrow[Rightarrow, to path=(U) -- (D)]{}   
            \arrow[bend left=50]{r}[name=W]{f'}         
            \arrow[bend right=50]{r}[name=E,below]{g'}
    & 
    \bullet \arrow[Rightarrow,to path=(W) -- (E)]{}
            \arrow[Rightarrow,to path={(O) ..controls +(2.5,0.7) and +(2.5,-0.7).. (S)}]{}
\end{tikzcd}
\]
Or like this?
\[
\begin{tikzcd}
    \bullet \arrow[bend left=75]{rr}[name=O]{ff'} 
            \arrow[bend right=75]{rr}[name=S,swap]{gg'} 
            \arrow[bend left=50]{r}[name=U]{f}          
            \arrow[bend right=50]{r}[name=D,below]{g}
    & 
    \bullet \arrow[Rightarrow, to path=(U) -- (D)]{}   
            \arrow[bend left=50]{r}[name=W]{f'}         
            \arrow[bend right=50]{r}[name=E,below]{g'}
    & 
    \bullet \arrow[Rightarrow,to path=(W) -- (E)]{}
            \arrow[Rightarrow, shorten >=2pt, shorten <=3pt,
                to path={(O) ..controls +(.4,-1) and +(.4,1).. (S)}]{}
\end{tikzcd}
\]
\end{document}