I have been trying to learn about snappy's method for encoding once-punctured torus bundles (http://www.math.uic.edu/t3m/SnapPy/manifold.html#snappy.Manifold). As you can see from the link, they are imported via the Manifold() function.

I have looked through documentation on the snappy website and much of the twister website. I am having trouble finding a reference for the encoding ‘b++LLR’, ‘b+-llR’, ‘bo-RRL’, ‘bn+LRLR’.

Following the literature (see for example http://arxiv.org/pdf/math/0406242.pdf), I am guessing that $L$ and $R$ correspond to writing an element in $SL(2,\mathbb{Z})$ as a word in

$L = \begin{pmatrix} 1 & 0 \\\\ 1 & 1 \end{pmatrix}$ and $R = \begin{pmatrix} 1 & 1 \\\\ 0 & 1 \end{pmatrix}$ with lower case elements used for inverses.

However, what to the b++, b+-, bn+ and bo- denote?