Is $\mathsf{DTIME}(n) = \mathsf{DTIME}(2n)$?
From the comment: 

In "Deterministic Turing Machines in the Range between Real-Time and Linear-Time" I found:

... if $r \in T^{−1}(DTM)$ and $r' \in o(r)$ then $DTIME(n+r') \subset DTIME(n+r)$ ...