What about neutral?
I was looking for such a list online some months ago, as my FCE students seemed to be a bit confused when they had to switch registers…and their specific connectors. After trying in vain to find a compared list, well, there might be one somewhere but I guess wasn’t lucky or patient enough to discover it, I gave up searching and started to make my own compilation.
As an English teacher, I tend to insist on developing my students’ formal/ academic exam writing skills (and I am sure I am not an exception), so it does not come as a surprise to me when they start using ‘therefore’ or ‘furthermore’ in their informal letters after writing so many formal tasks. Consequently, this list seems to have helped them organize and use connectors appropriately.
Again, feel free to download it and improve it, if you like.