As a non-native English speaker, I found the use of linking words lists very inspiring. I printed this cheatsheet and carry it with me along with the paper draft of my thesis for immediate access.
I also took an afternoon to brush up on my English (which, I believe, was already fine to begin with) and ended up reading most sections on this Guide to Grammar and Writing. In particular, I paid special attention to the page on Transitions, and it might help you too. On this page, they show how you can turn this hard-to-follow paragraph:
The ancient Egyptians were masters of preserving dead people's bodies
by making mummies of them. Mummies several thousand years old have
been discovered nearly intact. The skin, hair, teeth, fingernails and
toenails, and facial features of the mummies were evident. It is
possible to diagnose the disease they suffered in life, such as
smallpox, arthritis, and nutritional deficiencies. The process was
remarkably effective. Sometimes apparent were the fatal afflictions of
the dead people: a middle-aged king died from a blow on the head, and
polio killed a child king. Mummification consisted of removing the
internal organs, applying natural preservatives inside and out, and
then wrapping the body in layers of bandages.
into this nicer one
The ancient Egyptians were masters of preserving dead people's bodies
by making mummies of them. In short, mummification consisted of
removing the internal organs, applying natural preservatives inside
and out, and then wrapping the body in layers of bandages. And the
process was remarkably effective. Indeed, mummies several thousand
years old have been discovered nearly intact. Their skin, hair, teeth,
fingernails and toenails, and facial features are still evident. Their
diseases in life, such as smallpox, arthritis, and nutritional
deficiencies, are still diagnosable. Even their fatal afflictions are
still apparent: a middle-aged king died from a blow on the head; a
child king died from polio.
There are others resources grouped into "Word & Sentence Level", "Paragraph Level", "Essay & Research Paper Level".
Finally, if you need help writing transition paragraphs between sections, I'm not sure whether resources exist about this. I would suggest thinking about the high-level view of your work and reminding yourself (and the reader) why the previous section exists, why we are going to start the next one, and how they are connected within the big picture. During this paragraph, imagine your reader all of a sudden stops and says: "why the hell am I reading this already?" -- this is your chance to remind them.