We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are\documentclass[12pt]{minimal}
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				\begin{document}$${\mathcal {B}}$$\end{document}B-Canjar for any countably directed unbounded family\documentclass[12pt]{minimal}
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				\begin{document}$${\mathcal {B}}$$\end{document}Bof the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that\documentclass[12pt]{minimal}
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				\begin{document}$${\mathfrak {b}}=\omega _1$$\end{document}b=ω1in every extension by the above forcing notions.