The phrase "actually equivalent" is correct and usable in written English.
It can be used to clarify that two things are the same or have the same value or meaning, often in a context of comparison or explanation.
Example: "In mathematical terms, the two expressions are actually equivalent, despite their different appearances."
Alternatives: "truly equal" or "genuinely the same".
The way Obama and Romney employed these stereotypes are not actually equivalent.
"This is actually equivalent to mis-selling because, after all, people signed up on this agreement in 2012.
The value of the constant depends on the heat flux between the already solidified shell and the cooling media surrounding it and is actually equivalent to the solidified shell's thickness after one minute namely, about 20 millimetres when solidifying steel.
To clarify: the figure of 20m Swedish kroner (which is actually equivalent to about £1.9m, not £19m), was a rough estimate for annual spending on cycling programmes before the start of Malmö's current transport plan.
Moreover, it follows that (1.2) also implies (1.1), and hence, (1.1) and (1.2) are actually equivalent.
Hence, the almost automorphy investigated in [12] is actually equivalent to the ∇-almost automorphy.
To have 80% probability that this equivalence will occur when the two infusion therapies are actually exactly equivalent requires 70 patients per arm, assuming a standard deviation of 2 points within each arm (obtained from pilot work).
You have to have 1,000 windmills to actually be equivalent to one nuclear power plant," she told the audience.
They're actually the equivalent of the e-mails and phone calls from Fox News-crazed Tea Partiers demanding that their members of Congress stop at nothing to save the nation from the totalitarian horror of the Kenyan socialist apocalypse.
It sounds dangerous, but it's actually the equivalent of a covered call from a risk-reward standpoint.
For example, at the micro-scale it is possible to unify behaviors which appear different phenomenologically but actually possess equivalent dynamics.
