I find the mdi-transfer icon very useful to identify it with data transfer. They would be very useful left, right-left, up, down and up-down to identify different forms of data transfer such as reading, writing or reading / writing data.
mdi-transfer icon is made by @Templarian , I don't know if these variants are easy to make, but they would be useful.
I know that a lot of people don't like hearing this...but you can just transform them using CSS.
But I'm not using this icon in web design, but in a desktop application in WPF (I know that I can rotate the text too). As there are several left / right icons (like mdi-arrow-expand-left, mdi-arrow-left, mdi-arrow-left-bold...), I thought it would not be bad to have them in the case of transfer.
In title changing you forgot transfer-left-right and transfer-up-down to duplex data transfer.
Looking at the data points for transfer, I noticed that we could move the three points on the triangle to be on-grid. It's a bit hard to notice on this image but the difference is demonstrated in Figure 1. I have implemented that change in all the others.


Updated / Added. 馃槃 Breaking change unfortunately.
Thank you @MrGrigri for these new icons!
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I know that a lot of people don't like hearing this...but you can just transform them using CSS.