Transitional devices are like bridges between parts of your paper. They are cues that help the reader to interpret ideas in the way that you, as a writer, want them to understand. Transitional devices help you carry over a thought from one sentence to another, from one idea to another, or from one paragraph to another with words or phrases. And finally, transitional devices link your sentences and paragraphs together smoothly so that there are no abrupt jumps or breaks between ideas. 
There are several types of transitional devices, and each category leads your reader to make certain connections or assumptions about the areas you are connecting. Some lead your reader forward and imply the "building" of an idea or thought, while others make your reader compare ideas or draw conclusions from the preceding thoughts.
Here is a list of some common transitional devices that can be used to cue your reader in a given way.

To Add:

and, again, and then, besides, equally important, finally, further, furthermore, nor, too, next, lastly, what's more, moreover, in addition, first (second, etc.),

To Compare:

whereas, but, yet, on the other hand, however, nevertheless, on the other hand, on the contrary, by comparison, where, compared to, up against, balanced against, vis a vis, but, although, conversely, meanwhile, after all, in contrast, although this may be true

To Prove:

because, for, since, for the same reason, obviously, evidently, furthermore, moreover, besides, indeed, in fact, in addition, in any case, that is

To Show Exception:

yet, still, however, nevertheless, in spite of, despite, of course, once in a while, sometimes

To Show Time:

immediately, thereafter, soon, after a few hours, finally, then, later, previously, formerly, first (second, etc.), next, and then

To Repeat:

in brief, as I have said, as I have noted, as has been noted,

To Emphasize:

definitely, extremely, obviously, in fact, indeed, in any case, absolutely, positively, naturally, surprisingly, always, forever, perennially, eternally, never, emphatically, unquestionably, without a doubt, certainly, undeniably, without reservation

To Show Sequence:

first, second, third, and so forth. A, B, C, and so forth. next, then, following this, at this time, now, at this point, after, afterward, subsequently, finally, consequently, previously, before this, simultaneously, concurrently, thus, therefore, hence, next, and then, soon

To Give an Example:

for example, for instance, in this case, in another case, on this occasion, in this situation, take the case of, to demonstrate, to illustrate, as an illustration, to illustrate

To Summarize or Conclude:

in brief, on the whole, summing up, to conclude, in conclusion, as I have shown, as I have said, hence, therefore, accordingly, thus, as a result, consequently, on the whole,