Notice that the stitched fibrations discussed in Example 6.14 are more general than the ones constructed in Theorem 6.15. We illustrate this with an example. Let $U^{-}$ and $U^{+}$ be two “half annuli” of the same width but of different radii (as depicted in Figure 10). If $b^{\pm}=(b_{1}^{\pm},b_{2}^{\pm})$ denote coordinates on $U^{\pm}$ and we let $\Lambda^{\pm}=\langle{db_{1}^{\pm}},{db_{2}^{\pm}}\rangle_{\mathbb{Z}}$, then we can glue together $X^{+}=T^{*}U^{+}/\Lambda^{+}$ and $X^{-}=T^{*}U^{-}/\Lambda^{-}$ after choosing suitable invariants and applying the usual method of Theorem 6.11. We first glue the lower boundaries of $X^{+}$ and $X^{-}$ and then the upper boundaries, (as indicated by the arrows in Figure 10). This produces a stitched fibration of the type discussed in Example 6.14, in fact we would obtain a total space $X$ which fibres over a base obtained as the result of the gluing of the two half annuli, which is clearly diffeomorphic to an annulus. The fibration is not of the type constructed in Theorem 6.15. There are two main differences between the two constructions. In the examples from Theorem 6.15 action coordinates extend continuously to the whole annulus and the symplectic form on the total space is exact. These two facts do not hold in the example just described, in fact if the symplectic form were exact then the action coordinates would extend continuously to the whole annulus (to show this one can use an argument similar to the one used in Proposition 4.11).