after a little bit working, I found that Singapore style is preferable for my needs. Anyway the problem is still there.
I tried to include the mini-frame bullets in the sidebar using
\useoutertheme[subsection=false]{miniframes}
I added it to the preamble of my swp, which now looks like:
\newenvironment{stepenumerate}{\begin{enumerate}[<+->]}{\end{enumerate}}
\newenvironment{stepenumerate}{\begin{enumerate}[<+->]}{\end{enumerate}}
\newenvironment{stepitemize}{\begin{itemize}[<+->]}{\end{itemize} }
\newenvironment{stepenumeratewithalert}{\begin{enumerate}[<+-| alert@+>]}{\end{enumerate}}
\newenvironment{stepitemizewithalert}{\begin{itemize}[<+-| alert@+>]}{\end{itemize}}
\usetheme{Singapore}
\definecolor{unime}{rgb}{.93,.9,.0}
\usecolortheme[named=unime]{structure}
\setbeamerfont{footnote}{size=\tiny}
\useoutertheme{split}
\setbeamertemplate { items } [ball]
\definecolor{lside}{rgb}{.7,.0,.0}
\definecolor{leftFootlineColor}{rgb}{.54,.17, .89}
\useoutertheme{sidebar}
\setbeamercolor{frametitle}{bg=unime}
\setbeamercolor{section in head/foot}{bg=leftFootlineColor}
\logo {\includegraphics[scale=0.35]{uni}}
\setbeamertemplate{sidebar canvas left} [vertical shading]
[top=lside, bottom=lside]
\useoutertheme[subsection=false]{miniframes}
\DeclareGraphicsExtensions{.pdf,.png,.jpg}
\graphicspath{ {c:/} }
\input{tcilatex}
The output looks like this:

What I would like is to have the mini-frames bullets in the sidebar on the left instead of the name of each subsection. This would be more convenient if each section contains many subsections.
I hope I explained my case better now.
Thanks
Dario