\begin{tikzpicture}[cross line/.style={preaction={draw=white,->,line width=6pt}}]
\node (S)  at (0,0) {a};
\node (2)  at (0,4) {b};
\node (P)  at (4,0) {c};
\node (P2) at (4,4) {d};

\node (w)  at (2,2) {a1};
\node (W)  at (2,6) {b1};
\node (Pw) at (6,2) {c1};
\node (PW) at (6,6) {d1};

\draw[->](S)  -- (2);
\draw[->](S)  -- (P);
\draw[->](P)  -- (P2);

\draw[->](w)  -- (W);
\draw[->](w)  -- (Pw);
\draw[->](W)  -- (PW);
\draw[->](Pw) -- (PW);

\draw[->](S)  -- (w);
\draw[->](P)  -- (Pw);

\draw[->](2)  -- (W);
\draw[->](P2) -- (PW);
\draw[cross line,->] (2)  -- (P2);
\end{tikzpicture}

lines crossing each other (and making way for each other) in tikz

LaTeX