Here I use a macro approach, \connect{text}{lines}, where lines is the multiple of baselineskip to the connecting line. It can be a non-integer if there are added vertical spaces to contend with (e.g., \topskip and such).
Because the decoration is employed using the tabto package, the \connect{}{} macro can be issued at any place on the starting line of the connection.
EDITED to handle negative <lines> argument, which can reach upward. This can be useful to connect to display math, for which \connect is not valid.
\documentclass{article}
\usepackage{stackengine,tabto}
\newlength\tmplen
\setstackEOL{\cr}
\newcommand\connect[2]{%
\setstackgap{S}{0pt}%
\tabto*{0in}%
\setlength\tmplen{\dimexpr#2\baselineskip-\baselineskip}%
\setlength\tmplen{.5\tmplen}%
\ifdim\tmplen>0pt\relax
\smash{\raisebox{2.5pt}{\makebox[0pt][r]{%
\Shortunderstack[l]{%
\smash{\raisebox{-2.7pt}{\rarrow}}\cr
\protect\rule{.5pt}{\tmplen}\cr
\makebox[0pt]{#1\strut}\cr
\protect\rule{.5pt}{\tmplen}%
\smash{\raisebox{-2.4pt}{\rarrow}}\cr
}%
}}}%
\else
\setlength\tmplen{-\tmplen}%
\smash{\raisebox{2.5pt}{\makebox[0pt][r]{%
\Shortstack[l]{%
\smash{\raisebox{-2.7pt}{\rarrow}}\cr
\protect\rule{.5pt}{\tmplen}\cr
\makebox[0pt]{#1\strut}\cr
\protect\rule{.5pt}{\tmplen}%
\smash{\raisebox{-2.4pt}{\rarrow}}\cr
}%
}}}%
\fi
\tabto{\TabPrevPos}%
}
\def\rarrow{$\kern-.7pt{-}\kern-2pt{-}\kern-2pt{\rightarrow}$}
\begin{document}
\noindent\connect{OR}{4}\textbf{Blabla text here}\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
\noindent\textbf{Blabla text here}\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
\noindent\connect{AND}{6}\textbf{Blabla text here}\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
\noindent\textbf{Blabla text here}\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
Blabla text here\par
\[
y = mx + b
\]
Blabla text here\par
Blabla text here\par
\noindent \connect{Math!}{-1.8}Blabla text here\par
\end{document}

\documentclass{...}and ending with\end{document}. – May 04 '15 at 08:40