Eliminate space before \begin{itemize}

The way to fix this sort of problem is to redefine the relevant list environment. The enumitem package is my favourite way to do this sort of thing; it has many options and parameters that can be varied, either for all lists or for each list individually.

Here's how to do (something like) what it is I think you want:

\usepackage{enumitem}
\setlist{nolistsep}

or

\usepackage{enumitem}
\setlist{nosep}

Try \vspace{-5mm} before the itemize.

Use \vspace{-\topsep} before \begin{itemize}.

Use \setlength{\parskip}{0pt} \setlength{\itemsep}{0pt plus 1pt} after \begin{itemize}.

And for the space after the list, use \vspace{-\topsep} after \end{itemize}.

\vspace{-\topsep}
\begin{itemize}
  \setlength{\parskip}{0pt}
  \setlength{\itemsep}{0pt plus 1pt}
  \item ...
  \item ...
\end{itemize}
\vspace{-\topsep}