Controling left margin when dealing with tikz picture, or better yet - centering tikz picture properly

Question

I have the following tikzpicture:

\documentclass{article}

\usepackage{parskip}
\usepackage{amssymb}
\usepackage[fleqn]{amsmath}
\usepackage{tikz}
\usepackage{relsize}

\begin{document}

    \begin{center}
    \begin{tikzpicture}[scale=0.9]


    % % % % % % % % left % % % % % % % %
    \draw (-11.7,0.5) node {$\mathlarger{\mathlarger{\mathlarger{f=}}}$};

    % small rectangles
    \draw (-11,0) rectangle (-9,1) node[pos=0.5] {\large$\pi_{S_1}(I)$};
    \draw (-8.6,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};
    \draw (-8.2,0) rectangle (-6.2,1) node[pos=0.5] {\large$\pi_{S_2}(I)$};
    \draw (-5.8,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};

    \draw (-4.7,0.5) node {\huge$.\hspace{10pt}.\hspace{10pt}.$};

    \draw (-3.6,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};

    \draw (-3.2,0) rectangle (-1.2,1) node[pos=0.5] {\large$\pi_{S_n}(I)$};


    % big rectangle
    \draw (-9.5,3) rectangle (-2.7,4) node[pos=0.5] {\large\large\large$I$};

    % arrows
    \draw[<-] (-8.5,2.8) -- (-10,1.2);
    \draw[<-] (-6.5,2.8) -- (-7,1.2);
    \draw[<-] (-3.7,2.8) -- (-2.2,1.2);
    \draw (-10,2) node {$\mathlarger{\mathlarger{\beta^{-1}}}$};


    % % % % % % % % right % % % % % % % %
    \draw (1.2,0.5) node {$\mathlarger{\mathlarger{\mathlarger{f\,'=}}}$};

    % small rectangles
    \draw (1.9,0) rectangle (3.9,1) node[pos=0.5] {\large$\pi_{S\,'_1}(I\,')$};
    \draw (4.3,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};
    \draw (4.7,0) rectangle (6.7,1) node[pos=0.5] {\large$\pi_{S\,'_2}(I\,')$};
    \draw (7.1,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};

    \draw (8.2,0.5) node {\huge$.\hspace{10pt}.\hspace{10pt}.$};

    \draw (9.3,0.5) node {$\mathlarger{\mathlarger{\mathlarger{\bowtie}}}$};

    \draw (9.7,0) rectangle (11.7,1) node[pos=0.5] {\large$\pi_{S\,'_n}(I\,')$};


    % big rectangle
    \draw (3.4,3) rectangle (10.2,4) node[pos=0.5] {\large\large\large$I\,'$};

    % arrows
    \draw[->] (4.4,2.8) -- (2.9,1.2);
    \draw[->] (6.4,2.8) -- (5.9,1.2);
    \draw[->] (9.2,2.8) -- (10.7,1.2);
    \draw (2.9,2) node {$\mathlarger{\mathlarger{\beta}}$};

    \end{tikzpicture}
    \end{center}

\end{document}

The above produces this:

As you probably noticed, this is not what I intended when I used the \begin{center}\end{center} tags...

Is there a way to force the picture to be centered regardless of the left margin?
In other words, how do I tell the picture to ignore the margin and to center the whole thing properly?

Thanks in advance!