Parametrized Cichoń's diagram and small sets

We parametrize Cichoń's diagram and show how cardinals from Cichoń's diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of ${\displaystyle w^w\times 2^w}$ and continuous functions ${\displaystyle e,f:w^w\to w^w}$ such that  • N is ${\displaystyle G_{\delta }}$ and ${\displaystyle \{N_x:x\in w^w\}}$, the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of ${\displaystyle 2^w}$;  • M is ${\displaystyle F_{\sigma }}$ and ${\displaystyle \{M_x:x\in w^w\}}$ is a basis for the ideal of meager subsets of ${\displaystyle 2^w}$;  •${\displaystyle \forall x,y{N}_{e\left(x\right)}\subseteq N_y\Rightarrow M_x\subseteq M_{f\left(y\right)}}$. From this we derive that for a separable metric space X,  •if for all Borel (resp. ${\displaystyle G_{\delta }}$) sets ${\displaystyle B\subseteq X\times 2^w}$ with all vertical sections null, ${\displaystyle {\cup }_{x\in X}{B}_x}$ is null, then for all Borel (resp. ${\displaystyle F_{\sigma }}$) sets ${\displaystyle B\subseteq X\times 2^w}$ with all vertical sections meager, ${\displaystyle {\cup }_{x\in X}{B}_x}$ is meager;  •if there exists a Borel (resp. a "nice" ${\displaystyle G_{\delta }}$) set ${\displaystyle B\subseteq X\times 2^w}$ such that ${\displaystyle \{B_x:x\in X\}}$ is a basis for measure zero sets, then there exists a Borel (resp. ${\displaystyle F_{\sigma }}$) set ${\displaystyle B\subseteq X\times 2^w}$ such that ${\displaystyle \{B_x:x\in X\}}$ is a basis for meager sets