Left-align math

If you want them left aligned you need to indicate the alignment point be inserting a & at the beginning of the line:

Note:

• If you want them flush with the margin, you need a trailing & on at least one line as in the MWE below.
• The showframe package was used to just show the margins.

• If you want all equations in the document left aligned you can use the [fleqn] class option, and then the length \mathindent can be adjusted to control the amount of the indent.

  \documentclass[fleqn]{article}
  \setlength{\mathindent}{1cm}
  

Code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{showframe}

\begin{document}
\begin{flalign*}
&(0, (2, q_1), (0, q_1)) \rightarrow (0, (0, q_1), (1, q_2)) \rightarrow (0, (1, q_2), (2, q_2)) \rightarrow \\
&(0, (2, q_2), (0, q_2)) \rightarrow (0, (0, q_2), (1, q_3)) \rightarrow (0, (1, q_3), (2, q_3)) \rightarrow \\
&\vdots \\
&(0, (2, q_i), (0, q_i)) \rightarrow (0, (0, q_i), (1, q_{i + 1})) \rightarrow (0, (1, q_{i + 1}), (2, q_{i + 1})) \rightarrow \\
&\vdots &
\end{flalign*}
\end{document}

---

Without the trailing &, you still get the equations left aligned but with a small indent:

I'd add to @PeterGrill's solution that you'd probably want to align the arrows, too. You can do so by adding ampersands, one per column (except the first) and one per alignment point (including the first). For 4 columns you hence end up with 7 ampersands. Similar to the original document, an additional space has been inserted into the rightmost column, while for aesthetic reasons, the dots have been indented.

\documentclass{article}
\usepackage{amsmath}
\usepackage{lipsum} 

\begin{document}    
\lipsum[75]
%
\begin{flalign*}
&(0, (2, q_1), (0, q_1)) 
    &&\rightarrow (0, (0, q_1), (1, q_2)) 
    &&\rightarrow (0, (1, q_2), (2, q_2)) 
    &&\rightarrow \qquad\\    %\qquad: space to shift the column leftwards
&(0, (2, q_2), (0, q_2)) 
    &&\rightarrow (0, (0, q_2), (1, q_3)) 
    &&\rightarrow (0, (1, q_3), (2, q_3)) 
    &&\rightarrow\\
&\quad \vdots &&&&&&\\
&(0, (2, q_i), (0, q_i)) 
    &&\rightarrow (0, (0, q_i), (1, q_{i + 1})) 
    &&\rightarrow (0, (1, q_{i + 1}), (2, q_{i + 1})) 
    &&\rightarrow\\
&\quad \vdots &&&&&&
\end{flalign*}
%
\lipsum[75]         

\end{document}