I understand you need images right where you want them. I also had same condition once. But, then, you have to understand that you always are left with some uncontrollable blank spaces due to forced formatting with 'float' package.
However, I can tell you how to get your sections and texts get stuck to each other without unnecessary whitespaces. You need to add something like this:
\usepackage[compact]{titlesec} % you need this package
\titlespacing{\section}{0pt}{0pt}{0pt} % this reduces space between (sub)sections to 0pt, for example
\AtBeginDocument{% % this will reduce spaces between parts (above and below) of texts within a (sub)section to 0pt, for example - like between an 'eqnarray' and text
\setlength\abovedisplayskip{0pt}
\setlength\belowdisplayskip{0pt}}
These will let you reduce spaces in the overall text. For the images, I am not entirely sure how them to stick with text the way you can do with text. Still, try this (along with the float package):
\usepackage[rawfloats=true]{floatrow}
\restylefloat{figure} % this, I think, will reduce spaces between images and text.
The text part should work. But, I am not entirely sure about the images, sorry.
Also, if you specifically want to reduce space between two texts/images, you can also try writing (as the last resort)
\vspace{-3mm}
This will reduce vertical space by 3mm. Choose any size. But, again, there will be spaces that will not be reduced by any of these simply because of the formatting constraints, like for example, if you have some widetext in a revtex4 file, you will get some unwanted spaces due to that, as fitting the widetext is a mess, sometimes.
I hope this helps!
[H], the figure will drop onto the next page if it doesn't fit on the current page, creating a large space. Try deleting the[H]option: do the spaces go away? – Ian Thompson May 28 '15 at 11:57