How to write above a line in a tikzpicture

How to write above a line in a tikzpicture

How could I write just above the blue lines of this tikzpicture?
\begin{tikzpicture}[
    scale=5,
    IS/.style={blue, thick},
    LM/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
        outer sep=-1pt},
]
% axis
\draw[axis,-] (2.5,0) node(xline)[right] {$O_B$} -|
                (0,2.5) node(yline)[left] {$w$};
\draw[axis,-](2.5,0)--(2.5,2.5);
 \node (0,0) [left]{$O_A$};
  \draw[-, Blue] (0,2)--(1.4,.6)
\draw[-, Blue] (2.5,2)--(.8,.6);
   \draw[dashed] (0,.87) node[left] {$w_0^*$}--(2.5,.87) node[right] {$w_0^*$};
  \node[dot,label=above:$\epsilon_0$] at (1.13,.87) (int1) {};
\draw[dashed] (1.13,0) node[below]{$E_0$}--(1.13,0.87);
\end{tikzpicture}
I would like something like as the "ABC" and "CBA" are from this picture.