$$\alpha - D - (+)$$-glucose and $$\beta - D - (+) - $$glucose are

In carbohydrates the terms epimer, anomer, conformer and enantiomer have very specific structural meanings. Let us recall each one briefly before classifying $$\alpha - D - (+)$$-glucose and $$\beta - D - (+)$$-glucose.

1. Conformers
Conformations differ only by rotation about single bonds (e.g., staggered vs eclipsed ethane, chair vs boat cyclohexane). A change of configuration at a stereogenic centre is not involved.

2. Enantiomers
Enantiomers are non-superimposable mirror images. All chiral centres invert (R⇌S) simultaneously, giving opposite optical rotation signs.

3. Epimers
Epimers are diastereomers that differ in configuration at one of several stereogenic centres other than the anomeric carbon. For example, D-glucose vs D-mannose differ only at C-2 → they are C-2 epimers.

4. Anomers
When a monosaccharide cyclises, the carbonyl carbon becomes a new chiral centre called the anomeric carbon. Two stereoisomers differing only in the configuration at this anomeric carbon are called anomers and are denoted $$\alpha$$ and $$\beta$$. In the D-series:
• $$\alpha$$ = the OH at the anomeric carbon is trans to the CH2OH group (i.e., axial down in Haworth).
• $$\beta$$ = the OH is cis to the CH2OH group (equatorial up in Haworth).

Applying the definitions
$$\alpha - D - (+)$$-glucose and $$\beta - D - (+)$$-glucose have identical configuration at C-2, C-3, C-4 and C-5 (all the original stereocentres of D-glucose). They differ only at the freshly created anomeric centre (C-1) that arose upon ring closure of the open-chain aldehyde form. Hence they are neither conformers, nor enantiomers (mirror images), nor ordinary epimers (since the differing centre is specifically the anomeric carbon).

Therefore, they are anomers.

Option C which is: anomers