If I understand you right I think you can accomplish what you want by using minipages. You might need to futz with the spacings and widths, but something like this works in my test:
\begin{minipage}[c]{0.38\textwidth}
\begin{xy}
(0,-20)="a", (0,0)="b"
\ar@{<.||} @<24mm> "a";"b"
\ar@^{<.||} @<16mm> "a";"b"
\ar@_{<.||} @<8mm> "a";"b"
\ar@0{<.||} "a";"b"
\ar@1{<.||} @<-8mm> "a";"b"
\ar@2{<.||} @<-16mm> "a";"b"
\ar@3{<.||} @<-24mm> "a";"b"
\end{xy}
\end{minipage}
\hspace{0.03\textwidth}
\begin{minipage}[c]{0.05\textwidth}
~~~~~\Large =
\end{minipage}
\hspace{0.08\textwidth}
\begin{minipage}[c]{0.44\textwidth}
\begin{xy}
(0,-20)="a", (0,0)="b"
\ar@{<.||} @<24mm> "a";"b"
\ar@^{<.||} @<16mm> "a";"b"
\ar@_{<.||} @<8mm> "a";"b"
\ar@0{<.||} "a";"b"
\ar@1{<.||} @<-8mm> "a";"b"
\ar@2{<.||} @<-16mm> "a";"b"
\ar@3{<.||} @<-24mm> "a";"b"
\end{xy}
\end{minipage}